Totally convex algebras
Pumplün, Dieter ; Röhrl, Helmut
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 205-235 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1992-01-01
Classification:  46H05,  46H10,  46H20,  46H99,  46K05,  46K99,  46M15,  46M99 
@article{118490,
     author = {Dieter Pumpl\"un and Helmut R\"ohrl},
     title = {Totally convex algebras},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {205-235},
     zbl = {0763.46036},
     mrnumber = {1189653},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118490}
}

Pumplün, Dieter; Röhrl, Helmut. Totally convex algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 205-235. http://gdmltest.u-ga.fr/item/118490/

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