A note on the positivity of inverse operators acting on C⋆-algebras

IF 1 3区数学 Q1 MATHEMATICS Linear Algebra and its Applications Pub Date : 2024-12-16 DOI:10.1016/j.laa.2024.12.006

Jochen Glück , Ulrich Groh

引用次数: 0

Abstract

For a positive and invertible linear operator T acting on a C^⋆-algebra, we give necessary and sufficient criteria for the inverse operator

T^{- 1}

to be positive, too. Moreover, a simple counterexample shows that

T^{- 1}

need not be positive even if T is unital and its spectrum is contained in the unit circle.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.

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