Annals of Functional Analysis

Sherman type theorem on C*-algebras

Marek Niezgoda

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In this paper, a new definition of majorization for C*-algebras is introduced. Sherman’s inequality is extended to self-adjoint operators and positive linear maps by applying the method of premajorization used for comparing two tuples of objects. A general result in a matrix setting is established. Special cases of the main theorem are studied. In particular, a HLPK-type inequality is derived.

Article information

Ann. Funct. Anal., Volume 8, Number 4 (2017), 425-434.

Received: 14 August 2016
Accepted: 16 November 2016
First available in Project Euclid: 13 May 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A63: Operator inequalities
Secondary: 26D15: Inequalities for sums, series and integrals 15B48: Positive matrices and their generalizations; cones of matrices

self-adjoint operator positive linear map operator convex function Sherman’s inequality majorization


Niezgoda, Marek. Sherman type theorem on $C^{\ast}$ -algebras. Ann. Funct. Anal. 8 (2017), no. 4, 425--434. doi:10.1215/20088752-2017-0007.

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