Some characterizations of Hermitian Banach algebras
type: Item
instance of: scholarly article
title: Some characterizations of Hermitian Banach algebras
zbMATH Open document ID: 1402.46036
publication date: 2018-02-14T00:00:00Z
review text: A \(^*\)-algebra \(A\) is said to be Hermitian if \(\mathrm{Sp}(a)\subseteq\mathbb{R}\) for every \(a=a^*\in A\). In this paper, the author proves many new results concerning the properties of Hermitian Banach \(^*\)-algebras. A sample result is Corollary 4.5, which says that, for a Hermitian Banach \(^*\)-algebra \(A\), if \(A_+\) does not contain zero-divisors, then the spectrum of each self-adjoint element of \(A\) is an interval.
reviewed by: Hung Le Pham
Mathematics Subject Classification ID: 46K05
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 6838820
zbMATH Keywords: Hermitian algebras
zbMATH Keywords: convex cones
zbMATH Keywords: positive elements
zbMATH Keywords: algebraic zero-divisors
author: Mohamed Amine Nejjari
MaRDI profile type: Publication
full work available at URL: s12215-016-0253-y
OpenAlex ID: W2479390217
cites work: Q3215824
cites work: Q4433332
cites work: On a natural ordering in strictly real Banach algebras
cites work: The natural ordering on a strictly real Banach algebra
cites work: Banach algebras with involution
DOI: 10.1007/S12215-016-0253-Y
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 6838820