×
Dragomir, Sever S.

Some inequalities of Furuta’s type for functions of operators defined by power series. (English) Zbl 1343.47021

Acta Univ. Sapientiae, Math. 6, No. 2, 162-177 (2014).
Author’s abstract: Generalizations of Kato and Furuta inequalities for power series of bounded linear operators in Hilbert spaces are given. Applications for normal operators and some functions of interest such as the exponential, hyperbolic and trigonometric functions are provided as well.
Reviewer: Omar Hirzallah (Zarqa)

MSC:

47A63 Linear operator inequalities
47A99 General theory of linear operators

Keywords:

bounded linear operator; operator inequality; Kato inequality; function of normal operator; Euclidian norm; numerical radius
PDFBibTeX XMLCite
\textit{S. S. Dragomir}, Acta Univ. Sapientiae, Math. 6, No. 2, 162--177 (2014; Zbl 1343.47021)
Full Text: DOI
OA License

References:

[1] W. Arveson, A Short Course on Spectral Theory, 2002, Springer-Verlag Inc., New York.; · Zbl 0997.47001
[2] S. S. Dragomir, The hypo-Euclidean norm of an n-tuple of vectors in inner product spaces and applications, J. Inequal. Pure Appl. Math., 8 (2) (2007), Article 52, 22 pp.; · Zbl 1138.46015
[3] M. Fujii, C.-S. Lin, R. Nakamoto, Alternative extensions of Heinz-Kato- Furuta inequality, Sci. Math., 2 (2) (1999), 215{221.;} · Zbl 0961.47006
[4] M. Fujii and T. Furuta, Lowner-Heinz, Cordes and Heinz-Kato inequalities, Math. Japon., 38 (1) (1993), 73{78.;} · Zbl 0784.47013
[5] M. Fujii, E. Kamei, C. Kotari and H. Yamada, Furuta’s determinant type generalizations of Heinz-Kato inequality, Math. Japon., 40 (2) (1994), 259{267;} · Zbl 0805.47014
[6] M. Fujii, Y.O. Kim, Y. Seo, Further extensions of Wielandt type Heinz- Kato-Furuta inequalities via Furuta inequality, Arch. Inequal. Appl., 1 (2) (2003), 275{283.;} · Zbl 1045.47011
[7] M. Fujii, Y. O. Kim, M. Tominaga, Extensions of the Heinz-Kato-Furuta inequality by using operator monotone functions, Far East J. Math. Sci. (FJMS), 6 (3) (2002), 225{238.;} · Zbl 1044.47007
[8] M. Fujii, R. Nakamoto, Extensions of Heinz-Kato-Furuta inequality, Proc. Amer. Math. Soc., 128 (1) (2000), 223{228.;} · Zbl 0937.47022
[9] M. Fujii, R. Nakamoto, Extensions of Heinz-Kato-Furuta inequality. II., J. Inequal. Appl., 3 (3) (1999), 293{302.;} · Zbl 0937.47019
[10] T. Furuta, Equivalence relations among Reid, Lowner-Heinz and Heinz- Kato inequalities, and extensions of these inequalities, Integral Equations Operator Theory, 29 (1) (1997), 1{9.;} · Zbl 0901.47013
[11] T. Furuta, Determinant type generalizations of Heinz-Kato theorem via Furuta inequality, Proc. Amer. Math. Soc., 120 (1) (1994), 223{231.;} · Zbl 0804.47023
[12] T. Furuta, An extension of the Heinz-Kato theorem, Proc. Amer. Math. Soc., 120 (3) (1994), 785{787.;} · Zbl 0804.47022
[13] G. Helmberg, Introduction to Spectral Theory in Hilbert Space, John Wiley & Sons, Inc. -New York, 1969.; · Zbl 0177.42401
[14] T. Kato, Notes on some inequalities for linear operators, Math. Ann., 125 (1952), 208-212.; · Zbl 0048.35301
[15] F. Kittaneh, Notes on some inequalities for Hilbert space operators, Publ. Res. Inst. Math. Sci., 24 (2) (1988), 283{293.;} · Zbl 0655.47009
[16] F. Kittaneh, Norm inequalities for fractional powers of positive operators, Lett. Math. Phys., 27 (4) (1993), 279{285.;} · Zbl 0895.47003
[17] C.-S. Lin, On Heinz-Kato-Furuta inequality with best bounds, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math., 15 (1) (2008), 93{101.;} · Zbl 1189.47018
[18] C.-S. Lin, On chaotic order and generalized Heinz-Kato-Furuta-type inequality, Int. Math. Forum, 2 (37-40) (2007), 1849{1858.;} · Zbl 1151.47027
[19] C.-S. Lin, On inequalities of Heinz and Kato, and Furuta for linear operators, Math. Japon., 50 (3) (1999), 463{468.;} · Zbl 0945.47011
[20] C.-S. Lin, On Heinz-Kato type characterizations of the Furuta inequality. II., Math. Inequal. Appl., 2 (2) (1999), 283{287.;} · Zbl 0937.47020
[21] C. A. McCarthy, cp. Israel J. Math., 5(1967), 249-271.; · Zbl 0156.37902
[22] G. Popescu, Unitary invariants in multivariable operator theory, Mem. Amer. Math. Soc., 200 (941) (2009), vi+91 pp.; · Zbl 1180.47010
[23] M. Uchiyama, Further extension of Heinz-Kato-Furuta inequality, Proc. Amer. Math. Soc., 127 (10) (1999), 2899{2904.;} · Zbl 0931.47016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.