Edit Profile Hansen, Frank-Peter Compute Distance To: Compute Author ID: hansen.frank-peter Published as: Hansen, Frank; Hansen, Frank-Peter External Links: MGP · ORCID Documents Indexed: 60 Publications since 1977, including 3 Books Reviewing Activity: 9 Reviews all top 5 Co-Authors 41 single-authored 4 Pedersen, Gert Kjærgård 3 Tomiyama, Jun 2 Cai, Liang 2 Pečarić, Josip 1 Araki, Huzihiro 1 Audenaert, Koenraad M. R. 1 Effros, Edward George 1 Gibilisco, Paolo 1 Gyntelberg, Jacob 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 7 Linear Algebra and its Applications 6 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 38 Operator theory (47-XX) 19 Real functions (26-XX) 11 Functional analysis (46-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Quantum theory (81-XX) 6 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 46 Publications have been cited 578 times in 351 Documents Cited by ▼ Year ▼ Jensen’s inequality for operators and Loewner’s theorem. Zbl 0473.47011Hansen, Frank; Pedersen, Gert Kjaergard 121 1982 An operator inequality. Zbl 0407.47012Hansen, Frank 56 1980 Jensen’s operator inequality. Zbl 1051.47014Hansen, Frank; Pedersen, Gert K. 56 2003 Jensen’s operator inequality and its converses. Zbl 1151.47025Hansen, Frank; Pečarić, Josip; Perić, Ivan 27 2007 Metric adjusted skew information. Zbl 1205.94058Hansen, Frank 26 2008 Extensions of Lieb’s concavity theorem. Zbl 1157.47305Hansen, Frank 21 2006 The fast track to Löwner’s theorem. Zbl 1284.26011Hansen, Frank 21 2013 Non-commutative perspectives. Zbl 1308.47014Effros, E. G.; Hansen, Frank 18 2014 Operator convex functions of several variables. Zbl 0902.47013Hansen, Frank 17 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 13 2004 Operator monotone functions of several variables. Zbl 1035.47005Hansen, Frank 13 2003 The Wigner-Yanase entropy is not subadditive. Zbl 1111.82006Hansen, Frank 12 2007 Regular operator mappings and multivariate geometric means. Zbl 1308.47022Hansen, Frank 12 2014 Differential analysis of matrix convex functions. Zbl 1116.26006Hansen, Frank; Tomiyama, Jun 11 2007 Metric-adjusted skew information: convexity and restricted forms of superadditivity. Zbl 1194.94173Cai, Liang; Hansen, Frank 11 2010 Perturbation formulas for traces on \(C^*\)-algebras. Zbl 0829.46043Hansen, Frank; Pedersen, Gert K. 11 1995 Differential analysis of matrix convex functions. II. Zbl 1167.26307Hansen, Frank; Tomiyama, Jun 10 2009 Jensen’s trace inequality in several variables. Zbl 1049.46037Hansen, Frank; Pedersen, Gert K. 8 2003 Jensen’s operator inequality for functions of several variables. Zbl 0956.47009Araki, Huzihiro; Hansen, Frank 8 2000 Selfadjoint means and operator monotone functions. Zbl 0461.47009Hansen, Frank 8 1981 Inequalities for quantum skew information. Zbl 1161.81317Audenaert, Koenraad; Cai, Liang; Hansen, Frank 8 2008 Trace functions with applications in quantum physics. Zbl 1291.81072Hansen, Frank 7 2014 Means and concave products of positive semi-definite matrices. Zbl 0495.47021Hansen, Frank 7 1983 Non-commutative Hardy inequalities. Zbl 1188.47017Hansen, Frank 6 2009 Operator inequalities associated with Jensen’s inequalities. Zbl 1040.47012Hansen, Frank 6 2000 Characterisation of matrix entropies. Zbl 1330.60017Hansen, Frank; Zhang, Zhihua 5 2015 Generalized noncommutative Hardy and Hardy-Hilbert type inequalities. Zbl 1204.26026Hansen, Frank; Krulić, Kristina; Pečarić, Josip; Persson, Lars-Erik 4 2010 Jensen’s operator inequality for functions of two variables. Zbl 0870.47013Hansen, Frank 4 1997 Functions of matrices with nonnegative entries. Zbl 0745.15013Hansen, Frank 4 1992 Quantum entropy derived from first principles. Zbl 1360.81036Hansen, Frank 3 2016 Convexity of quantum \(\chi ^{2}\)-divergence. Zbl 1256.81023Hansen, Frank 3 2011 Multivariate extensions of the Golden-Thompson inequality. Zbl 1337.15019Hansen, Frank 3 2015 Expected utility with subjective events. Zbl 1254.91103Gyntelberg, Jacob; Hansen, Frank 3 2012 Selfpolar norms on an indefinite inner product space. Zbl 0458.46017Hansen, Frank 3 1980 Perspectives and completely positive maps. Zbl 1454.47023Hansen, Frank 2 2017 Extrema for concave operator mappings. Zbl 0815.47014Hansen, Frank 2 1994 Some operator monotone functions. Zbl 1156.81341Hansen, Frank 2 2009 A note on quantum entropy. Zbl 1413.81006Hansen, Frank 2 2016 The Moyal product and spectral theory for a class of infinite dimensional matrices. Zbl 0748.46043Hansen, Frank 2 1990 Perturbations of centre-fixing dynamical systems. Zbl 0374.46054Hansen, Frank; Olesen, Dorte 2 1978 Convex trace functions of several variables. Zbl 1034.47005Hansen, Frank 2 2002 Golden-Thompson’s inequality for deformed exponentials. Zbl 1323.82003Hansen, Frank 1 2015 WYD-like skew information measures. Zbl 1272.82005Hansen, Frank 1 2013 Monotone trace functions of several variables. Zbl 1093.47016Hansen, Frank 1 2005 Variational representations related to Tsallis relative entropy. Zbl 1459.94078Shi, Guanghua; Hansen, Frank 1 2020 Variational representations related to Tsallis relative entropy. Zbl 1459.94078Shi, Guanghua; Hansen, Frank 1 2020 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 1 2015 Non-commutative perspectives. Zbl 1308.47014Effros, E. G.; Hansen, Frank 18 2014 Regular operator mappings and multivariate geometric means. Zbl 1308.47022Hansen, Frank 12 2014 Trace functions with applications in quantum physics. Zbl 1291.81072Hansen, Frank 7 2014 The fast track to Löwner’s theorem. Zbl 1284.26011Hansen, Frank 21 2013 WYD-like skew information measures. Zbl 1272.82005Hansen, Frank 1 2013 Expected utility with subjective events. Zbl 1254.91103Gyntelberg, Jacob; Hansen, Frank 3 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 4 2010 Differential analysis of matrix convex functions. II. Zbl 1167.26307Hansen, Frank; Tomiyama, Jun 10 2009 Non-commutative Hardy inequalities. Zbl 1188.47017Hansen, Frank 6 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 27 2007 The Wigner-Yanase entropy is not subadditive. Zbl 1111.82006Hansen, Frank 12 2007 Differential analysis of matrix convex functions. Zbl 1116.26006Hansen, Frank; Tomiyama, Jun 11 2007 Extensions of Lieb’s concavity theorem. Zbl 1157.47305Hansen, Frank 21 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 13 2004 Jensen’s operator inequality. Zbl 1051.47014Hansen, Frank; Pedersen, Gert K. 56 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 8 2000 Operator inequalities associated with Jensen’s inequalities. Zbl 1040.47012Hansen, Frank 6 2000 Operator convex functions of several variables. Zbl 0902.47013Hansen, Frank 17 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 7 1983 Jensen’s inequality for operators and Loewner’s theorem. Zbl 0473.47011Hansen, Frank; Pedersen, Gert Kjaergard 121 1982 Selfadjoint means and operator monotone functions. Zbl 0461.47009Hansen, Frank 8 1981 An operator inequality. Zbl 0407.47012Hansen, Frank 56 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 348 Authors 28 Hansen, Frank-Peter 23 Hiai, Fumio 15 Petz, Dénes 13 Uchiyama, Mitsuru 9 Moslehian, Mohammad Sal 9 Pečarić, Josip 8 Kian, Mohsen 8 Nikoufar, Ismail 8 Osaka, Hiroyuki 7 Bikchentaev, Aĭrat Midkhatovich 7 Dinh Trung Hoa 7 Furuta, Takayuki 7 Kim, Sejong 7 Tomiyama, Jun 6 Chansangiam, Pattrawut 6 Gibilisco, Paolo 6 Isola, Tommaso 5 Furuichi, Shigeru 5 Kosaki, Hideki 5 Mićić, Jadranka 5 Wada, Shuhei 4 Bhatia, Rajendra 4 Cai, Liang 4 Krnić, Mario 4 Lim, Yongdo 4 Luo, Shunlong 4 Najafi, Hamed 4 Pavić, Zlatko 4 Pedersen, Gert Kjærgård 4 Rashid, Mohammad Hussein Mohammad 4 Shi, Guanghua 4 Virosztek, Dániel 3 Anjidani, Ehsan 3 Audenaert, Koenraad M. R. 3 Aujla, Jaspal Singh 3 Bakherad, Mojtaba 3 Cao, Huaixin 3 Dragomir, Sever Silvestru 3 Jiang, Tianpei 3 Lee, Hosoo 3 Moradi, Hamid Reza 3 Mosonyi, Milán 3 Niezgoda, Marek 3 Pálfia, Miklós 3 Pascoe, James Eldred 3 Pereverzev, Sergei V. 3 Rastëgin, Alekseĭ Èduardovich 3 Ruskai, Mary Beth 3 Sano, Takashi 3 Sendov, Hristo S. 3 Seo, Yuki 3 Tikhonov, Oleg Evgen’evich 3 Tomamichel, Marco 3 Tropp, Joel A. 3 Vasudeva, Harkrishan Lal 3 Yanagi, Kenjiro 2 Ando, Tsuyoshi 2 Andruchow, Esteban 2 Berta, Mario 2 Besenyei, Ádám 2 Bourin, Jean-Christophe 2 Braha, Naim Latif 2 Carlen, Eric Anders 2 Chen, Jein-Shan 2 Dubin, Daniel A. 2 Dumitru, Raluca 2 Ebadian, Ali 2 Eshaghi Gordji, Madjid 2 Fan, Yajing 2 Farenick, Douglas R. 2 Franco, Jose A. 2 Gao, Fugen 2 Garayev, Mübariz Tapdıgoğlu 2 Guillot, Dominique 2 Hennings, Mark A. 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 H. 2 Mikić, Rozarija 2 Pan, Shaohua 2 Pietrzycki, Paweł 2 Pitrik, József 2 Rajaratnam, Bala 2 Ricard, Éric 2 Saunderson, James 2 Shamohammadi, Moosa 2 Shao, Jingjing 2 Silvestrov, Sergei D. 2 Skripka, Anna 2 Tanahashi, Kôtarô 2 Temme, Kristan 2 Uchiyama, Atsushi 2 Yamazaki, Takeaki 2 Yuan, Jiangtao ...and 248 more Authors all top 5 Cited in 107 Serials 71 Linear Algebra and its Applications 17 Journal of Mathematical Physics 15 Linear and Multilinear Algebra 14 Journal of Mathematical Analysis and Applications 13 Letters in Mathematical Physics 13 Journal of Functional Analysis 13 Positivity 13 Journal of Inequalities and Applications 11 Journal of Statistical Physics 10 Proceedings of the American Mathematical Society 10 International Journal of Mathematics 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 5 Advances in Mathematics 5 Integral Equations and Operator Theory 5 Quantum Information Processing 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 3 Communications in Mathematical Physics 3 Mathematische Annalen 3 Abstract and Applied Analysis 3 Infinite Dimensional Analysis, Quantum Probability and Related Topics 3 Annales Henri Poincaré 3 Complex Analysis and Operator Theory 2 Glasgow Mathematical Journal 2 Siberian Mathematical Journal 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 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 Studia Mathematica 1 Theoretical and Mathematical Physics 1 Arkiv för Matematik 1 Acta Mathematica 1 Acta Mathematica Vietnamica 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 Numerical Functional Analysis and Optimization 1 Proceedings of the Japan Academy. Series A 1 Quaestiones Mathematicae 1 Results in Mathematics 1 Theory and Decision 1 Tohoku Mathematical Journal. Second Series 1 Systems & Control Letters 1 Statistics & Probability Letters 1 Acta Mathematica Hungarica 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 Computational and Applied Mathematics 1 Georgian Mathematical Journal 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 Annals of Mathematics. Second Series 1 Communications of the Korean Mathematical Society 1 Acta Mathematica Sinica. English Series 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 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 Proceedings of the Steklov Institute of Mathematics 1 Journal of Physics A: Mathematical and Theoretical 1 Operators and Matrices 1 Banach Journal of Mathematical Analysis 1 Asian-European Journal of Mathematics 1 Journal of Nonlinear Science and Applications 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Analysis and Mathematical Physics 1 Bulletin of Mathematical Sciences 1 Axioms 1 Chamchuri Journal of Mathematics ...and 7 more Serials all top 5 Cited in 40 Fields 220 Operator theory (47-XX) 99 Linear and multilinear algebra; matrix theory (15-XX) 89 Functional analysis (46-XX) 79 Quantum theory (81-XX) 60 Real functions (26-XX) 54 Information and communication theory, circuits (94-XX) 14 Probability theory and stochastic processes (60-XX) 12 Statistical mechanics, structure of matter (82-XX) 8 Statistics (62-XX) 8 Operations research, mathematical programming (90-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Convex and discrete geometry (52-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Combinatorics (05-XX) 5 Functions of a complex variable (30-XX) 5 Difference and functional equations (39-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Differential geometry (53-XX) 4 Partial differential equations (35-XX) 4 Computer science (68-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-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 Approximations and expansions (41-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