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