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Title: Totally convex algebras (English)
Author: Pumplün, Dieter
Author: Röhrl, Helmut
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 33
Issue: 2
Year: 1992
Pages: 205-235
Category: math
Summary: By definition a totally convex algebra $A$ is a totally convex space $|A|$ equipped with an associative multiplication, i.e\. a morphism $\mu :|A|\otimes |A|\longrightarrow |A|$ of totally convex spaces. In this paper we introduce, for such algebras, the notions of ideal, tensor product, unitization, inverses, weak inverses, quasi-inverses, weak quasi-inverses and the spectrum of an element and investigate them in detail. This leads to a considerable generalization of the corresponding notions and results in the theory of Banach spaces. (English)
Keyword: totally convex algebra
Keyword: Eilenberg-Moore algebra
Keyword: Banach algebra
Keyword: ideal
Keyword: (weak) inverse
Keyword: spectrum
MSC: 46H05
MSC: 46H10
MSC: 46H20
MSC: 46H99
MSC: 46K05
MSC: 46K99
MSC: 46M15
MSC: 46M99
idZBL: Zbl 0763.46036
idMR: MR1189653
Date available: 2009-01-08T17:55:08Z
Last updated: 2012-04-30
Stable URL:
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