An Operator Extension of Čebyšev Inequality-Reference-Cited by-同舟云学术

An Operator Extension of Čebyšev Inequality

Published:2017-07-26 Issue:2 Volume:25 Page:135-147
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Moradi Hamid Reza¹,Omidvar Mohsen Erfanian¹,Dragomir Silvestru Sever²

Affiliation:

1. Mashhad Branch, Islamic Azad University, Mashhad , Iran

2. College of Engineering & Science, Victoria University, PO Box 14428, Melbourne City , MC 8001, Australia

Abstract

Abstract Some operator inequalities for synchronous functions that are related to the čebyšev inequality are given. Among other inequalities for synchronous functions it is shown that ∥ø(f(A)g(A)) - ø(f(A))ø(g(A))∥ ≤ max{║ø(f2(A)) - ø2(f(A))║, ║ø)G2(A)) - ø2(g(A))║} where A is a self-adjoint and compact operator on B(ℋ ), f, g ∈ C (sp (A)) continuous and non-negative functions and ø: B(ℋ ) → B(ℋ ) be a n-normalized bounded positive linear map. In addition, by using the concept of quadruple D-synchronous functions which is generalizes the concept of a pair of synchronous functions, we establish an inequality similar to čebyšev inequality.

Publisher

Walter de Gruyter GmbH

Reference19 articles.

1. [1] W. Audeh, and F. Kittaneh, Singular value inequalities for compact op- erators, Linear Algebra Appl. 437(10) (2012), 2516-2522.

2. [2] T. Ando, Topics on operator inequalities. Sapporo: Division of Applied Mathematics, Research Institute of Applied Electricity, Hokkaido Univer- sity, (1978).

3. [3] R. Bhatia, and C. Davis, More operator versions of the Schwarz inequality, Comm. Math. Phys. 215(2) (2000), 239-244.

4. [4] R. Bhatia, Positive Deffnite Matrices, Princeton University Press, (2007).

5. [5] P.L. Čebyšev, O pribli_zennyh vyra_zenijah odnih integralov ćerez drugie, Soob_sćenija i protokoly zasedani_i Matemmatićeskogo obćestva pri Imper- atorskom Har'kovskom Universitete, No. 2, pp. 9398; Polnoe sobranie soćineni_i P. L. Čebyševa. Moskva Leningrad, 1948a, (1882), 128-131.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Further inequalities related to synchronous and asynchronous functions;Filomat;2023

2. Further results on Jensen-type inequalities;Issues of Analysis;2019-11

3. Cebysev’s type inequalities and power inequalities for the Berezin number of operators;Filomat;2019