Improved Young and Heinz operator inequalities with Kantorovich constant
Анотація
УДК 517.9
Вдосконаленi операторнi нерiвностi Янга та Хайнца з константою Канторовича
Отримано ряд покращень нерівності Янга за допомогою константи Канторовича.
Ці покращені нерівності використовуються для встановлення відповідних операторних нерівностей у просторі Гільберта та деяких нових нерівностей,
що включають норми Гільберта – Шмідта для матриць.
Посилання
M. Bakherad, M. Krnic, M. S. Moslehian, ´ Reverse Young-type inequalities for matrices and operators, Rocky Mountain J. Math., 46, № 4, 1089 – 1105 (2016), https://doi.org/10.1216/RMJ-2016-46-4-1089 DOI: https://doi.org/10.1216/RMJ-2016-46-4-1089
C. Conde, Young type inequalities for positive operators, Ann. Funct. Anal., 4, № 2, 144 – 152 (2013), https://doi.org/10.15352/afa/1399899532 DOI: https://doi.org/10.15352/afa/1399899532
J. I. Fujii, M. Fujii, Y. Seo, Z. Hongliang, Recent developments of matrix versions of the arithmetic-geometric meaninequality, Ann. Funct. Anal., 7, № 1, 102 – 117 (2016), https://doi.org/10.1215/20088752-3429400 DOI: https://doi.org/10.1215/20088752-3429400
M. Fujii, R. Nakamoto, Refinements of Hölder – McCarthy inequality and Young inequality, Adv. Oper. Theory, 1, № 2, 184 – 188 (2016), https://doi.org/10.22034/aot.1610.1037
T. Furuta, Invitation to linear operators. From matrices to bounded linear operators on a Hilbert space, Taylor & Francis, Ltd., London (2001), https://doi.org/10.1201/b16820 DOI: https://doi.org/10.1201/b16820
O. Hirzallah, F. Kittaneh, Matrix Young inequalities for the Hilbert – Schmidt norm, Linear Algebra and Appl., 308, 77 – 84 (2000), https://doi.org/10.1016/S0024-3795(99)00270-0 DOI: https://doi.org/10.1016/S0024-3795(99)00270-0
F. Kittaneh, On the convexity of the Heinz means, Integral. Equat. and Oper. Theory, 68, 519 – 527 (2010), https://doi.org/10.1007/s00020-010-1807-6 DOI: https://doi.org/10.1007/s00020-010-1807-6
M. Krnić, More accurate Young, Heinz, and Holder inequalities for matrices, Period Math. Hungar., 71, № 1, 78 – 91 (2015), https://doi.org/10.1007/s10998-015-0086-z DOI: https://doi.org/10.1007/s10998-015-0086-z
W. Liao, J. Wu, Improved Young and Heinz inequalities with the Kantorovich constant, J. Math. Inequal., 10, № 2, 559 – 570 (2016), https://doi.org/10.7153/jmi-10-44 DOI: https://doi.org/10.7153/jmi-10-44
D.S. Mitrinovic, J. Pečarić, A.M. Fink, Classical and new inequalities in analysis, Kluwer Acad. Publ., Dordrecht etc. (1993). DOI: https://doi.org/10.1007/978-94-017-1043-5
J. E. Pečarić, T. Furuta, J. Mićić Hot, Y. Seo, Mond – Pečarić method in operator inequalities, Element, Zagreb (2005).
M. Sababheh, D. Choi, A complete refinement of Young’s inequality, J. Math. Anal. and Appl., 440, № 1, 379 – 393 (2016), https://doi.org/10.1016/j.jmaa.2016.03.049 DOI: https://doi.org/10.1016/j.jmaa.2016.03.049
M. Sababheh, M. S. Moslehian, Advanced refinements of Young and Heinz inequalities, J. Number Theory, 172, 178 – 199 (2017), https://doi.org/10.1016/j.jnt.2016.08.009 DOI: https://doi.org/10.1016/j.jnt.2016.08.009
M. Shafiei, A. G. Ghazanfari, Numerous refinements of Polya and Heinz operator inequalities, Linear and Multilinear Algebra, 66, № 4, 852 – 860 (2018), https://doi.org/10.1080/03081087.2017.1329815 DOI: https://doi.org/10.1080/03081087.2017.1329815
J. G. Zhao, J. L. Wu, Operator inequalities involving improved Young and its reverse inequalities, J. Math. Anal. and Appl., 421, № 2, 1779 – 1789 (2015), https://doi.org/10.1016/j.jmaa.2014.08.032 DOI: https://doi.org/10.1016/j.jmaa.2014.08.032
L. Zou, Y. Jiang, Improved Heinz inequality and its application, J. Inequal. and Appl., 113 (2012); https://doi.org/10.1186/1029-242X-2012-113. DOI: https://doi.org/10.1186/1029-242X-2012-113
H. Zuo, G. Shi, M. Fujii, Refined Young inequality with Kantorovich constant, J. Math. Inequal., 5, № 4, 551 – 556 (2011), https://doi.org/10.7153/jmi-05-47 DOI: https://doi.org/10.7153/jmi-05-47
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