Tripotents in algebras: ideals and commutators
type: Item
instance of: scholarly article
title: Tripotents in algebras: ideals and commutators
DOI: 10.1134/S1995080222100109
author: Khattab Fawwaz
author: Rinat S. Yakushev
published in: Lobachevskii Journal of Mathematics
publication date: 2022-11-15T00:00:00Z
review text: An element \(A\) in algebra \(\mathcal{A}\) is said to be \(n\)-potent (\(n\in \mathbb{N}\)) if \(A^{n}=A\). For the particular cases \(n=2\) and \(n=3,\) we find the standard definitions of idempotents and tripotents, respectively. The main goal of this paper is to study \(n\)-potent elements in unital algebras. Obtaining in this way the compactness conditions for the product \(AB\) of a Hilbert space tripotents \(A\) and \(B\). Also, the authors discovered conditions assured that \(A+B\) is an idempotent.
reviewed by: Elhadj Dahia
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 47L35
zbMATH DE Number: 7617007
zbMATH Keywords: algebra
zbMATH Keywords: idempotent
zbMATH Keywords: tripotent
zbMATH Keywords: Hilbert space
zbMATH Keywords: linear operator
zbMATH Keywords: compact operator
MaRDI profile type: Publication
full work available at URL: s1995080222100109
OpenAlex ID: W4312663398
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description: scientific article; zbMATH DE number 7617007