Geodesic
Totally convex algebras
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 205-235.

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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.
Classification : 46H05, 46H10, 46H20, 46H99, 46K05, 46K99, 46M15, 46M99
Keywords: totally convex algebra; Eilenberg-Moore algebra; Banach algebra; ideal; (weak) inverse; spectrum 
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     title = {Totally convex algebras},
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Pumplün, Dieter; Röhrl, Helmut. Totally convex algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 205-235. http://geodesic.mathdoc.fr/item/CMUC_1992__33_2_a2/