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Totally convex algebras

Dieter PumplünHelmut Röhrl — 1992

Commentationes Mathematicae Universitatis Carolinae

By definition a totally convex algebra A is a totally convex space | A | equipped with an associative multiplication, i.eȧ morphism μ : | A | | A | | 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.

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