Dinh Trung Hoa, O. E. Tikhonov, “Weighted Monotonicity Inequalities for Traces on Operator Algebras”, Mat. Zametki, 88:2 (2010), 193–200; Math. Notes, 88:1 (2010), 177

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Matematicheskie Zametki, 2010, Volume 88, Issue 2, Pages 193–200
DOI: https://doi.org/10.4213/mzm8802 (Mi mzm8802)

This article is cited in 9 scientific papers (total in 9 papers)

Weighted Monotonicity Inequalities for Traces on Operator Algebras

Dinh Trung Hoa, O. E. Tikhonov

Kazan State University

Full-text PDF (463 kB) Citations (9)

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DOI: https://doi.org/10.4213/mzm8802

Abstract: We study inequalities of the form

$\tau(w(A)^{1/2}f(A)w(A)^{1/2})\le\tau(w(A)^{1/2}f(B)w(A)^{1/2}),\qquad A\le B,$
where

$\tau$ is a trace on a von Neumann algebra or a

$C^*$ -algebra,

$A$ and

$B$ are self-adjoint elements of the algebra in question,

$f$ and

$w$ are real-valued functions, and the “weight” function

$w$ is nonnegative.

Keywords: von Neumann algebra,

$C^*$ -algebra, trace, monotonicity, Hermitian matrix, weight function, self-adjoint element, tracial functional, Borel function.

Received: 20.05.2009

English version:
Mathematical Notes, 2010, Volume 88, Issue 1, Pages 177–182
DOI: https://doi.org/10.1134/S0001434610070175

Bibliographic databases:

Document Type: Article

UDC: 517.986

Language: Russian

Citation: Dinh Trung Hoa, O. E. Tikhonov, “Weighted Monotonicity Inequalities for Traces on Operator Algebras”, Mat. Zametki, 88:2 (2010), 193–200; Math. Notes, 88:1 (2010), 177–182

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm8802

https://doi.org/10.4213/mzm8802

https://www.mathnet.ru/eng/mzm/v88/i2/p193

This publication is cited in the following 9 articles:

Mariana Dalloul, “Characterization of Tracial Functionals by Inequalities for the Spread of a Matrix”, Lobachevskii J Math, 45:6 (2024), 2478
Airat M. Bikchentaev, Fuad Kittaneh, Mohammad Sal Moslehian, Yuki Seo, Forum for Interdisciplinary Mathematics, Trace Inequalities, 2024, 261
Airat Bikchentaev, Springer Proceedings in Mathematics & Statistics, 390, Infinite Dimensional Analysis, Quantum Probability and Applications, 2022, 279
Alhasan H. Fawwaz Kh., “Characterization of Tracial Functionals on Von Neumann Algebras”, Lobachevskii J. Math., 42:10, SI (2021), 2273–2279
Bikchentaev A.M. Sherstnev A.N., “Studies on Noncommutative Measure Theory in Kazan University (1968-2018)”, Int. J. Theor. Phys., 60:2, SI (2021), 585–596
Bikchentaev A.M. Abed S.A., “Projections and Traces on Von Neumann Algebras”, Lobachevskii J. Math., 40:9, SI (2019), 1260–1267
Dinh Trung Hoa, Osaka H., Tomiyama J., “Characterization of Operator Monotone Functions By Powers-Stormer Type Inequalities”, Linear Multilinear Algebra, 63:8 (2015), 1577–1589
An. An. Novikov, O. E. Tikhonov, “Characterization of central elements of operator algebras by inequalities”, Lobachevskii J Math, 36:2 (2015), 208
Dinh Trung Hoa, “On weighted monotonicity inequalities and characterizations of the traces”, Lobachevskii J Math, 33:2 (2012), 152

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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