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Some trace inequalities for convex functions of selfadjoint operators in Hilbert spaces
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Some new trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.
Abstract
Some new trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.
참고문헌 (47)
- T. Ando, "Matrix Young inequalities", Oper. Theory Adv. Appl, 75, pp.33~38 (1995)
- R. Bellman, "Some inequalities for positive definite matrices", General Inequalities 2, Proceedings of the 2nd International Conference on General Inequalities, pp.89~90 (1980), Birkhauser
- E. V. Belmega, "A generalization of a trace inequality for positive definite matrices", Aust. J. Math. Anal. Appl, 7(26), pp.5~ (2010)
- E. A. Carlen, "Entropy and the quantum", pp.73~140 (2010), Amer. Math. Soc
- D. Chang, "A matrix trace inequality for products of Hermitian matrices", J. Math. Anal. Appl, 237, pp.721~725 (1999)
- L. Chen, "Inequalities for singular values and traces", Linear Algebra Appl, 171, pp.109~120 (1992)
- I. D. Coop, "On matrix trace inequalities and related topics for products of Hermitian matrix", J. Math. Anal. Appl, 188, pp.999~1001 (1994)
- S. S. Dragomir, "A converse result for Jensen's discrete inequality via Gruss'inequality and applications in information theory", An. Univ. Oradea Fasc. Mat, 7, pp.178~189 (1999)
- S. S. Dragomir, "On a reverse of Jessen's inequality for isotonic linear functionals", J. Ineq. Pure & Appl. Math, 2(3) (2001)
- S. S. Dragomir, "A Gruss type inequality for isotonic linear functionals and applications", Demonstratio Math, 36(3), pp.551~562 (2003)
- S. S. Dragomir, "Bounds for the normalized Jensen functional", Bull. Austral. Math. Soc, 74(3), pp.471~476 (2006)
- S. S. Dragomir, "Bounds for the deviation of a function from the chord generated by its extremities", Bull. Aust. Math. Soc, 78(2), pp.225~248 (2008)
- S. S. Dragomir, "Gruss' type inequalities for functions of selfadjoint operators in Hilbert spaces", RGMIA Res. Rep. Coll, 11, pp.11~ (2008)
- S. S. Dragomir, "Some inequalities for convex functions of selfadjoint operators in Hilbert spaces", Filomat, 23(3), pp.81~92 (2009)
- S. S. Dragomir, "Some Jensen's type inequalities for twice differentiable functions of selfadjoint operators in Hilbert spaces", Filomat, 23(3), pp.211~222 (2009)
- S. S. Dragomir, "Some new Gruss' type inequalities for functions of selfadjoint operators in Hilbert spaces", Sarajevo J. Math, 6(18), pp.89~107 (2010)
- S. S. Dragomir, "New bounds for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces", Filomat, 24(2), pp.27~39 (2010)
- S. S. Dragomir, "Some Jensen's type inequalities for log-convex functions of selfadjoint operators in Hilbert spaces", Bull. Malays. Math. Sci. Soc, 34(3) (2011)
- S. S. Dragomir, "Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces", J. Ineq. & Appl, 2010 (2010)
- S. S. Dragomir, "Some Slater's type inequalities for convex functions of selfadjoint operators in Hilbert spaces", Rev. Un. Mat. Argentina, 52(1), pp.109~120 (2011)
- S. S. Dragomir, "Hermite-Hadamard's type inequalities for operator convex functions", Appl. Math. Comp, 218, pp.766~772 (2011)
- S. S. Dragomir, "Hermite-Hadamard's type inequalities for convex functions of selfadjoint operators in Hilbert spaces", Res. Rep. Coll., 13(2), pp.1~ (2010)
- S. S. Dragomir, "New Jensen's type inequalities for differentiable log-convex functions of selfadjoint operators in Hilbert spaces", Sarajevo J. Math, 19(1), pp.67~80 (2011)
- S. S. Dragomir, "Operator Inequalities of the Jensen, Cebysev and Gruss Type", pp.xii~121 (2012), Springer
- S. S. Dragomir, "Operator Inequalities of Ostrowski and Trapezoidal Type", pp.x~112 (2012), Springer
- S. S. Dragomir, "Some converse of Jensen's inequality and applications", Rev. Anal. Numer. Theor. Approx, 23(1), pp.71~78 (1994)
- S. Furuichi, "Refinements of the trace inequality of Belmega, Lasaulce and Debbah", Aust. J. Math. Anal. Appl, 7(2), pp.4~ (2010)
- T. Furuta, "Mond-Pecaric Method in Operator Inequalities. Inequalities for Bounded Selfadjoint Operators on a Hilbert Space" (2005), Element
- G. Helmberg, "Introduction to Spectral Theory in Hilbert Space" (1969), John Wiley
- 이현덕, "ON SOME MATRIX INEQUALITIES", 한국수학논문집, 16(4), pp.565~571 (2008), 강원경기수학회
- L. Liu, "A trace class operator inequality", J. Math. Anal. Appl, 328, pp.1484~1486 (2007)
- S. Manjegani, "Holder and Young inequalities for the trace of operators", Positivity, 11, pp.239~250 (2007)
- H. Neudecker, "A matrix trace inequality", J. Math. Anal. Appl, 166, pp.302~303 (1992)
- K. Shebrawi, "Operator norm inequalities of Minkowski type", J. Inequal. Pure Appl. Math, 9(1), pp.1~10 (2008)
- K. Shebrawi, "Trace inequalities for matrices", Bull. Aust. Math. Soc, 87, pp.139~148 (2013)
- B. Simon, "Trace Ideals and Their Applications" (1979), Cambridge University Press
- A. Matkovic, "A variant of Jensen's inequality of Mercer's type for operators with applications", Linear Algebra Appl, 418(2-3), pp.551~564 (2006)
- C. A. McCarthy, "cp", Israel J. Math, 5, pp.249~271 (1967)
- J. Micic, "Inequalities of Furuta and Mond-Pecaric", Math. Ineq. Appl, 2, pp.83~111 (1999)
- B. Mond, "Convex inequalities in Hilbert space", Houston J. Math, 19, pp.405~420 (1993)
- B. Mond, "On some operator inequalities", Indian J. Math, 35, pp.221~232 (1993)
- B. Mond, "Classical inequalities for matrix functions", Utilitas Math, 46, pp.155~166 (1994)
- S. Simic, "On a global upper bound for Jensen's inequality", J. Math. Anal. Appl, 343, pp.414~419 (2008)
- Z. Ulukok, "On some matrix trace inequalities", J. Inequal. Appl, 2010, pp.8~ (2010)
- X. Yang, "A matrix trace inequality", J. Math. Anal. Appl, 250, pp.372~374 (2000)
- X. M. Yang, "A matrix trace inequality", J. Math. Anal. Appl, 263, pp.327~331 (2001)
- Y. Yang, "A matrix trace inequality", J. Math. Anal. Appl, 133, pp.573~574 (1988)
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