<abstract xmlns="http://www.w3.org/1999/xhtml"> 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.</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.

An Operator Extension of Čebyšev Inequality

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"An Operator Extension of Čebyšev Inequality"}

Some operator inequalities for synchronous functions that are related to the čebyšev inequality are given. Among other inequalities for synchronous functions...

An Operator Extension of Čebyšev Inequality

Published Online: Sep 21, 2017

Page range: 135 - 147

Received: Oct 03, 2016

Accepted: Oct 24, 2016

DOI: https://doi.org/10.1515/auom-2017-0025

Keywords
čebyšev inequality, self-adjoint operators, synchronous (asynchronous) functions, functions of self-adjoint operators, positive linear map

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

An Operator Extension of Čebyšev Inequality

Published Online: Sep 21, 2017

Page range: 135 - 147

Received: Oct 03, 2016

Accepted: Oct 24, 2016

DOI: https://doi.org/10.1515/auom-2017-0025

Keywordsčebyšev inequality, self-adjoint operators, synchronous (asynchronous) functions, functions of self-adjoint operators, positive linear map

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
čebyšev inequality, self-adjoint operators, synchronous (asynchronous) functions, functions of self-adjoint operators, positive linear map