Edit Profile (opens in new tab) Hansen, Frank-Peter Compute Distance To: Compute Author ID: hansen.frank-peter Published as: Hansen, Frank; Hansen, Frank-Peter; Hansen, F. more...less External Links: MGP · ORCID Documents Indexed: 63 Publications since 1977, including 3 Books Reviewing Activity: 9 Reviews Co-Authors: 19 Co-Authors with 20 Joint Publications 913 Co-Co-Authors all top 5 Co-Authors 43 single-authored 4 Pedersen, Gert Kjærgård 3 Tomiyama, Jun 2 Cai, Liang 2 Gibilisco, Paolo 2 Pečarić, Josip 1 Araki, Huzihiro 1 Audenaert, Koenraad M. R. 1 Effros, Edward George 1 Gyntelberg, Jacob 1 Isola, Tommaso 1 Ji, Guoxing 1 Krulić Himmelreich, Kristina 1 Moslehian, Mohammad Sal 1 Najafi, Hamed 1 Olesen, Dorte 1 Perić, Ivan 1 Persson, Lars-Erik 1 Shi, Guanghua 1 Zhang, Zhihua all top 5 Serials 9 Linear Algebra and its Applications 7 Journal of Statistical Physics 4 Letters in Mathematical Physics 4 Mathematische Annalen 4 Publications of the Research Institute for Mathematical Sciences, Kyoto University 4 Annals of Functional Analysis 3 Bulletin of the London Mathematical Society 3 Mathematica Scandinavica 3 International Journal of Mathematics 3 JIPAM. Journal of Inequalities in Pure & Applied Mathematics 2 Proceedings of the American Mathematical Society 2 Proceedings of the National Academy of Sciences of the United States of America 2 The Australian Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Mathematica Japonica 1 Journal of the Mongolian Mathematical Society 1 Mathematical Physics, Analysis and Geometry 1 Positivity 1 Mathematical Inequalities & Applications 1 RIMS Kokyuroku 1 The B. E. Journal of Theoretical Economics 1 Proceedings of the Estonian Academy of Sciences all top 5 Fields 40 Operator theory (47-XX) 20 Real functions (26-XX) 13 Functional analysis (46-XX) 11 Quantum theory (81-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 8 Information and communication theory, circuits (94-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Mathematical logic and foundations (03-XX) 2 Group theory and generalizations (20-XX) 2 Probability theory and stochastic processes (60-XX) 1 Topological groups, Lie groups (22-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 49 Publications have been cited 638 times in 391 Documents Cited by ▼ Year ▼ Jensen’s inequality for operators and Loewner’s theorem. Zbl 0473.47011Hansen, Frank; Pedersen, Gert Kjaergard 126 1982 Jensen’s operator inequality. Zbl 1051.47014Hansen, Frank; Pedersen, Gert K. 61 2003 An operator inequality. Zbl 0407.47012Hansen, Frank 60 1980 Jensen’s operator inequality and its converses. Zbl 1151.47025Hansen, Frank; Pečarić, Josip; Perić, Ivan 31 2007 The fast track to Löwner’s theorem. Zbl 1284.26011Hansen, Frank 29 2013 Metric adjusted skew information. Zbl 1205.94058Hansen, Frank 26 2008 Non-commutative perspectives. Zbl 1308.47014Effros, E. G.; Hansen, Frank 22 2014 Extensions of Lieb’s concavity theorem. Zbl 1157.47305Hansen, Frank 22 2006 Operator convex functions of several variables. Zbl 0902.47013Hansen, Frank 18 1997 Trace functions as Laplace transforms. Zbl 1111.47022Hansen, Frank 14 2006 Gaps between classes of matrix monotone functions. Zbl 1047.26008Hansen, Frank; Ji, Guoxing; Tomiyama, Jun 14 2004 Regular operator mappings and multivariate geometric means. Zbl 1308.47022Hansen, Frank 13 2014 Operator monotone functions of several variables. Zbl 1035.47005Hansen, Frank 13 2003 Differential analysis of matrix convex functions. Zbl 1116.26006Hansen, Frank; Tomiyama, Jun 12 2007 The Wigner-Yanase entropy is not subadditive. Zbl 1111.82006Hansen, Frank 12 2007 Metric-adjusted skew information: convexity and restricted forms of superadditivity. Zbl 1194.94173Cai, Liang; Hansen, Frank 11 2010 Differential analysis of matrix convex functions. II. Zbl 1167.26307Hansen, Frank; Tomiyama, Jun 11 2009 Perturbation formulas for traces on \(C^*\)-algebras. Zbl 0829.46043Hansen, Frank; Pedersen, Gert K. 11 1995 On a correspondence between regular and non-regular operator monotone functions. Zbl 1178.47011Gibilisco, P.; Hansen, F.; Isola, T. 9 2009 Selfadjoint means and operator monotone functions. Zbl 0461.47009Hansen, Frank 9 1981 Trace functions with applications in quantum physics. Zbl 1291.81072Hansen, Frank 9 2014 Jensen’s operator inequality for functions of several variables. Zbl 0956.47009Araki, Huzihiro; Hansen, Frank 9 2000 Jensen’s trace inequality in several variables. Zbl 1049.46037Hansen, Frank; Pedersen, Gert K. 8 2003 Inequalities for quantum skew information. Zbl 1161.81317Audenaert, Koenraad; Cai, Liang; Hansen, Frank 8 2008 Means and concave products of positive semi-definite matrices. Zbl 0495.47021Hansen, Frank 8 1983 Non-commutative Hardy inequalities. Zbl 1188.47017Hansen, Frank 8 2009 Operator inequalities associated with Jensen’s inequalities. Zbl 1040.47012Hansen, Frank 6 2000 Generalized noncommutative Hardy and Hardy-Hilbert type inequalities. Zbl 1204.26026Hansen, Frank; Krulić, Kristina; Pečarić, Josip; Persson, Lars-Erik 5 2010 Characterisation of matrix entropies. Zbl 1330.60017Hansen, Frank; Zhang, Zhihua 5 2015 Expected utility with subjective events. Zbl 1254.91103Gyntelberg, Jacob; Hansen, Frank 4 2012 Functions of matrices with nonnegative entries. Zbl 0745.15013Hansen, Frank 4 1992 Jensen’s operator inequality for functions of two variables. Zbl 0870.47013Hansen, Frank 4 1997 Quantum entropy derived from first principles. Zbl 1360.81036Hansen, Frank 3 2016 Convexity of quantum \(\chi ^{2}\)-divergence. Zbl 1256.81023Hansen, Frank 3 2011 Selfpolar norms on an indefinite inner product space. Zbl 0458.46017Hansen, Frank 3 1980 Multivariate extensions of the Golden-Thompson inequality. Zbl 1337.15019Hansen, Frank 3 2015 Operator maps of Jensen-type. Zbl 06979791Hansen, Frank; Moslehian, Mohammad Sal; Najafi, Hamed 3 2018 Perspectives and completely positive maps. Zbl 1454.47023Hansen, Frank 2 2017 Some operator monotone functions. Zbl 1156.81341Hansen, Frank 2 2009 The Moyal product and spectral theory for a class of infinite dimensional matrices. Zbl 0748.46043Hansen, Frank 2 1990 Extrema for concave operator mappings. Zbl 0815.47014Hansen, Frank 2 1994 Perturbations of centre-fixing dynamical systems. Zbl 0374.46054Hansen, Frank; Olesen, Dorte 2 1978 Golden-Thompson’s inequality for deformed exponentials. Zbl 1323.82003Hansen, Frank 2 2015 Convex trace functions of several variables. Zbl 1034.47005Hansen, Frank 2 2002 Variational representations related to Tsallis relative entropy. Zbl 1459.94078Shi, Guanghua; Hansen, Frank 2 2020 A note on quantum entropy. Zbl 1413.81006Hansen, Frank 2 2016 WYD-like skew information measures. Zbl 1272.82005Hansen, Frank 1 2013 Monotone trace functions of several variables. Zbl 1093.47016Hansen, Frank 1 2005 Convex multivariate operator means. Zbl 07007598Hansen, Frank 1 2019 Variational representations related to Tsallis relative entropy. Zbl 1459.94078Shi, Guanghua; Hansen, Frank 2 2020 Convex multivariate operator means. Zbl 07007598Hansen, Frank 1 2019 Operator maps of Jensen-type. Zbl 06979791Hansen, Frank; Moslehian, Mohammad Sal; Najafi, Hamed 3 2018 Perspectives and completely positive maps. Zbl 1454.47023Hansen, Frank 2 2017 Quantum entropy derived from first principles. Zbl 1360.81036Hansen, Frank 3 2016 A note on quantum entropy. Zbl 1413.81006Hansen, Frank 2 2016 Characterisation of matrix entropies. Zbl 1330.60017Hansen, Frank; Zhang, Zhihua 5 2015 Multivariate extensions of the Golden-Thompson inequality. Zbl 1337.15019Hansen, Frank 3 2015 Golden-Thompson’s inequality for deformed exponentials. Zbl 1323.82003Hansen, Frank 2 2015 Non-commutative perspectives. Zbl 1308.47014Effros, E. G.; Hansen, Frank 22 2014 Regular operator mappings and multivariate geometric means. Zbl 1308.47022Hansen, Frank 13 2014 Trace functions with applications in quantum physics. Zbl 1291.81072Hansen, Frank 9 2014 The fast track to Löwner’s theorem. Zbl 1284.26011Hansen, Frank 29 2013 WYD-like skew information measures. Zbl 1272.82005Hansen, Frank 1 2013 Expected utility with subjective events. Zbl 1254.91103Gyntelberg, Jacob; Hansen, Frank 4 2012 Convexity of quantum \(\chi ^{2}\)-divergence. Zbl 1256.81023Hansen, Frank 3 2011 Metric-adjusted skew information: convexity and restricted forms of superadditivity. Zbl 1194.94173Cai, Liang; Hansen, Frank 11 2010 Generalized noncommutative Hardy and Hardy-Hilbert type inequalities. Zbl 1204.26026Hansen, Frank; Krulić, Kristina; Pečarić, Josip; Persson, Lars-Erik 5 2010 Differential analysis of matrix convex functions. II. Zbl 1167.26307Hansen, Frank; Tomiyama, Jun 11 2009 On a correspondence between regular and non-regular operator monotone functions. Zbl 1178.47011Gibilisco, P.; Hansen, F.; Isola, T. 9 2009 Non-commutative Hardy inequalities. Zbl 1188.47017Hansen, Frank 8 2009 Some operator monotone functions. Zbl 1156.81341Hansen, Frank 2 2009 Metric adjusted skew information. Zbl 1205.94058Hansen, Frank 26 2008 Inequalities for quantum skew information. Zbl 1161.81317Audenaert, Koenraad; Cai, Liang; Hansen, Frank 8 2008 Jensen’s operator inequality and its converses. Zbl 1151.47025Hansen, Frank; Pečarić, Josip; Perić, Ivan 31 2007 Differential analysis of matrix convex functions. Zbl 1116.26006Hansen, Frank; Tomiyama, Jun 12 2007 The Wigner-Yanase entropy is not subadditive. Zbl 1111.82006Hansen, Frank 12 2007 Extensions of Lieb’s concavity theorem. Zbl 1157.47305Hansen, Frank 22 2006 Trace functions as Laplace transforms. Zbl 1111.47022Hansen, Frank 14 2006 Monotone trace functions of several variables. Zbl 1093.47016Hansen, Frank 1 2005 Gaps between classes of matrix monotone functions. Zbl 1047.26008Hansen, Frank; Ji, Guoxing; Tomiyama, Jun 14 2004 Jensen’s operator inequality. Zbl 1051.47014Hansen, Frank; Pedersen, Gert K. 61 2003 Operator monotone functions of several variables. Zbl 1035.47005Hansen, Frank 13 2003 Jensen’s trace inequality in several variables. Zbl 1049.46037Hansen, Frank; Pedersen, Gert K. 8 2003 Convex trace functions of several variables. Zbl 1034.47005Hansen, Frank 2 2002 Jensen’s operator inequality for functions of several variables. Zbl 0956.47009Araki, Huzihiro; Hansen, Frank 9 2000 Operator inequalities associated with Jensen’s inequalities. Zbl 1040.47012Hansen, Frank 6 2000 Operator convex functions of several variables. Zbl 0902.47013Hansen, Frank 18 1997 Jensen’s operator inequality for functions of two variables. Zbl 0870.47013Hansen, Frank 4 1997 Perturbation formulas for traces on \(C^*\)-algebras. Zbl 0829.46043Hansen, Frank; Pedersen, Gert K. 11 1995 Extrema for concave operator mappings. Zbl 0815.47014Hansen, Frank 2 1994 Functions of matrices with nonnegative entries. Zbl 0745.15013Hansen, Frank 4 1992 The Moyal product and spectral theory for a class of infinite dimensional matrices. Zbl 0748.46043Hansen, Frank 2 1990 Means and concave products of positive semi-definite matrices. Zbl 0495.47021Hansen, Frank 8 1983 Jensen’s inequality for operators and Loewner’s theorem. Zbl 0473.47011Hansen, Frank; Pedersen, Gert Kjaergard 126 1982 Selfadjoint means and operator monotone functions. Zbl 0461.47009Hansen, Frank 9 1981 An operator inequality. Zbl 0407.47012Hansen, Frank 60 1980 Selfpolar norms on an indefinite inner product space. Zbl 0458.46017Hansen, Frank 3 1980 Perturbations of centre-fixing dynamical systems. Zbl 0374.46054Hansen, Frank; Olesen, Dorte 2 1978 all cited Publications top 5 cited Publications all top 5 Cited by 384 Authors 30 Hansen, Frank-Peter 25 Hiai, Fumio 15 Petz, Dénes 13 Uchiyama, Mitsuru 11 Moslehian, Mohammad Sal 10 Kian, Mohsen 9 Nikoufar, Ismail 9 Pečarić, Josip 8 Bikchentaev, Aĭrat Midkhatovich 8 Osaka, Hiroyuki 7 Dinh Trung Hoa 7 Furuta, Takayuki 7 Gibilisco, Paolo 7 Isola, Tommaso 7 Kim, Sejong 7 Tomiyama, Jun 6 Chansangiam, Pattrawut 6 Dragomir, Sever Silvestru 6 Furuichi, Shigeru 6 Moradi, Hamid Reza 6 Wada, Shuhei 5 Kosaki, Hideki 5 Lim, Yongdo 5 Mićić, Jadranka 4 Audenaert, Koenraad M. R. 4 Bhatia, Rajendra 4 Cai, Liang 4 Krnić, Mario 4 Luo, Shunlong 4 Najafi, Hamed 4 Pascoe, James Eldred 4 Pavić, Zlatko 4 Pedersen, Gert Kjærgård 4 Rashid, Mohammad Hussein Mohammad 4 Sababheh, Mohamad Suboh 4 Sano, Takashi 4 Seo, Yuki 4 Shi, Guanghua 4 Virosztek, Dániel 4 Yanagi, Kenjiro 3 Anjidani, Ehsan 3 Aujla, Jaspal Singh 3 Bakherad, Mojtaba 3 Braha, Naim Latif 3 Cao, Huaixin 3 Dumitru, Raluca 3 Franco, Jose A. 3 Garayev, Mübariz Tapdıgoğlu 3 Jiang, Tianpei 3 Kittaneh, Fuad 3 Lee, Hosoo 3 Mosonyi, Milán 3 Niezgoda, Marek 3 Pálfia, Miklós 3 Pereverzev, Sergei V. 3 Rastëgin, Alekseĭ Èduardovich 3 Ruskai, Mary Beth 3 Sendov, Hristo S. 3 Tanahashi, Kôtarô 3 Tikhonov, Oleg Evgen’evich 3 Tomamichel, Marco 3 Tropp, Joel A. 3 Vasudeva, Harkrishan Lal 3 Yamanci, Ulas 3 Yamazaki, Takeaki 3 Yuan, Jiangtao 2 Ando, Tsuyoshi 2 Andruchow, Esteban 2 Bedrani, Yassine 2 Berta, Mario 2 Besenyei, Ádám 2 Bourin, Jean-Christophe 2 Carlen, Eric Anders 2 Chen, Jein-Shan 2 Dadkhah, Ali 2 Dubin, Daniel A. 2 Ebadian, Ali 2 Eshaghi Gordji, Madjid 2 Fan, Yajing 2 Farenick, Douglas R. 2 Faulkner, Thomas 2 Gao, Fugen 2 Guillot, Dominique 2 Gurdal, Mehmet 2 Hennings, Mark A. 2 Hollands, Stefan 2 Hosseini, Mohsen Shah 2 Hoxha, Ilmi 2 Hwang, Jinmi 2 Imparato, Daniele 2 Ito, Masatoshi 2 Jain, Tanvi 2 Kamei, Eizaburo 2 Kastoryano, Michael J. 2 Khare, Apoorva 2 Larotonda, Gabriel 2 Lieb, Elliott Hershel 2 McCullough, Scott A. 2 Mikić, Rozarija 2 Moosavi, Baharak ...and 284 more Authors all top 5 Cited in 120 Serials 75 Linear Algebra and its Applications 18 Linear and Multilinear Algebra 17 Journal of Mathematical Physics 16 Journal of Mathematical Analysis and Applications 14 Journal of Statistical Physics 14 Letters in Mathematical Physics 14 Positivity 14 Journal of Inequalities and Applications 13 Journal of Functional Analysis 10 Proceedings of the American Mathematical Society 10 International Journal of Mathematics 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 6 Integral Equations and Operator Theory 5 Advances in Mathematics 5 Quantum Information Processing 4 Communications in Mathematical Physics 4 Reviews in Mathematical Physics 4 Transactions of the American Mathematical Society 4 Proceedings of the National Academy of Sciences of the United States of America 4 Annales Henri Poincaré 3 Mathematische Annalen 3 Siberian Mathematical Journal 3 Abstract and Applied Analysis 3 Infinite Dimensional Analysis, Quantum Probability and Related Topics 3 Complex Analysis and Operator Theory 2 Rocky Mountain Journal of Mathematics 2 Studia Mathematica 2 Acta Mathematica Vietnamica 2 Glasgow Mathematical Journal 2 Numerical Functional Analysis and Optimization 2 Results in Mathematics 2 Statistics & Probability Letters 2 Acta Mathematica Hungarica 2 Journal of Complexity 2 Aequationes Mathematicae 2 Russian Mathematics 2 Mathematical Physics, Analysis and Geometry 2 Mathematical Inequalities & Applications 2 Foundations of Computational Mathematics 2 Operators and Matrices 2 Annals of Functional Analysis 2 Problemy Analiza. Issues of Analysis 1 Indian Journal of Pure & Applied Mathematics 1 International Journal of Theoretical Physics 1 Journal d’Analyse Mathématique 1 Theoretical and Mathematical Physics 1 Arkiv för Matematik 1 Acta Mathematica 1 Applied Mathematics and Computation 1 Demonstratio Mathematica 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Economic Theory 1 Journal of Mathematical Economics 1 Journal of the Mathematical Society of Japan 1 Mathematische Nachrichten 1 Mathematica Scandinavica 1 Mathematica Slovaca 1 Mathematische Zeitschrift 1 Proceedings of the Japan Academy. Series A 1 Quaestiones Mathematicae 1 Theory and Decision 1 Tôhoku Mathematical Journal. Second Series 1 Systems & Control Letters 1 Bulletin of the Iranian Mathematical Society 1 Journal of Classification 1 Revista Matemática Iberoamericana 1 Journal of Theoretical Probability 1 Forum Mathematicum 1 Sugaku Expositions 1 Journal of Global Optimization 1 Mathematical Programming. Series A. Series B 1 Indagationes Mathematicae. New Series 1 New Zealand Journal of Mathematics 1 Applied and Computational Harmonic Analysis 1 Computational and Applied Mathematics 1 Georgian Mathematical Journal 1 Filomat 1 Bernoulli 1 Mathematical Communications 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete Dynamics in Nature and Society 1 New Journal of Physics 1 Communications de la Faculté des Sciences de l’Université d’Ankara. Séries A1. Mathematics and Statistics 1 Annals of Mathematics. Second Series 1 Communications of the Korean Mathematical Society 1 Acta Mathematica Sinica. English Series 1 Foundations of Science 1 Lobachevskii Journal of Mathematics 1 International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 1 Entropy 1 Computational Methods and Function Theory 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Hacettepe Journal of Mathematics and Statistics 1 Thai Journal of Mathematics 1 Mediterranean Journal of Mathematics 1 Fixed Point Theory and Applications 1 African Diaspora Journal of Mathematics 1 The Australian Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics, Analysis, Geometry ...and 20 more Serials all top 5 Cited in 40 Fields 244 Operator theory (47-XX) 108 Linear and multilinear algebra; matrix theory (15-XX) 98 Functional analysis (46-XX) 87 Quantum theory (81-XX) 70 Real functions (26-XX) 59 Information and communication theory, circuits (94-XX) 15 Probability theory and stochastic processes (60-XX) 13 Statistical mechanics, structure of matter (82-XX) 10 Statistics (62-XX) 9 Operations research, mathematical programming (90-XX) 8 Convex and discrete geometry (52-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Difference and functional equations (39-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Combinatorics (05-XX) 5 Functions of a complex variable (30-XX) 5 Partial differential equations (35-XX) 5 Differential geometry (53-XX) 5 Computer science (68-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Approximations and expansions (41-XX) 3 Integral transforms, operational calculus (44-XX) 3 Numerical analysis (65-XX) 2 Measure and integration (28-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Integral equations (45-XX) 2 General topology (54-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Relativity and gravitational theory (83-XX) 1 Systems theory; control (93-XX) Citations by Year