## Annals of Functional Analysis

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

### Sherman type theorem on ${C}^{*}$-algebras

#### Abstract

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

**Source**

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

**Dates**

Received: 14 August 2016

Accepted: 16 November 2016

First available in Project Euclid: 13 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.afa/1494640814

**Digital Object Identifier**

doi:10.1215/20088752-2017-0007

**Mathematical Reviews number (MathSciNet)**

MR3717165

**Zentralblatt MATH identifier**

06841324

**Subjects**

Primary: 47A63: Operator inequalities

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

**Keywords**

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

#### Citation

Niezgoda, Marek. Sherman type theorem on $C^{\ast}$ -algebras. Ann. Funct. Anal. 8 (2017), no. 4, 425--434. doi:10.1215/20088752-2017-0007. https://projecteuclid.org/euclid.afa/1494640814