## Dieter Pumpl\"un, Helmut R\"ohrl

*Totally convex algebras*

Comment.Math.Univ.Carolinae 33,2 (1992) 205-236. **Abstract:**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.

**Keywords:** totally convex algebra, Eilenberg-Moore algebra, Banach algebra, ideal, (weak) inverse, spectrum

**AMS Subject Classification:** 46H05, 46H10, 46H20, 46K05, 46M99

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