On \(TQ\)-algebras
type: Item
instance of: scholarly article
title: On \(TQ\)-algebras
zbMATH Open document ID: 1382.46033
author: Mati Abel
author: Yuliana de Jesús Zárate-Rodríguez
author: Lourdes Palacios F.
published in: Mediterranean Journal of Mathematics
publication date: 2017-11-09T00:00:00Z
review text: Let \(A\) be a topological algebra with unit \(e\). An element \(x\) in \(A\) is called left (right) topologically invertible if there is a net \((z_\alpha)\subset A\) with \(\lim_\alpha z_\alpha x=e\) (\(\lim_\alpha xz_\alpha=e\)). A left (right) \(TQ\)-algebra is a topological algebra for which the set of left (right) topologically invertible elements is open. The main result of the paper (Theorem 4.3) characterizes these algebras by providing several equivalent conditions. E.g., \(A\) is a left \(TQ\)-algebra if and only if its left topological spectral radius is continuous at \(0\), or if and only if it is upper semicontinuous. Other results concern the functional topological spectrum (when this spectrum is defined through multiplicative-linear functionals) and the question when a \(TQ\)-algebra is a \(Q\)-algebra (its set of invertible elements is open).
reviewed by: Wiesław Tadeusz Żelazko
Mathematics Subject Classification ID: 46H20
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 6804280
zbMATH Keywords: \(TQ\)-algebra
zbMATH Keywords: topological spectrum
zbMATH Keywords: topological spectral radius
zbMATH Keywords: topologically invertible elements
MaRDI profile type: Publication
full work available at URL: s00009-017-0983-x
OpenAlex ID: W2742224150
cites work: Advertive topological algebras
cites work: Q4658801
cites work: Properties ofTQ-algebras
cites work: Q5755119
cites work: Topological algebras with ascending or descending chain condition
cites work: Q4681228
cites work: Topological rings
cites work: Q4463865
cites work: Topologically \(Q\)-algebras, more
cites work: Q5518756
cites work: Q3730448
cites work: Q2999566
cites work: Q4257161
cites work: Q5631608
cites work: Q4350156
cites work: Polynomial completeness in locally multiplicatively-convex algebras
DOI: 10.1007/S00009-017-0983-X
description: scientific article; zbMATH DE number 6804280