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Zbl 1209.46023
Abel, Mati
Representations of topological algebras by projective limits. (English)
[J] Ann. Funct. Anal. AFA 1, No. 1, 144-157, electronic only (2010). ISSN 2008-8752/e

Summary: It is shown that (a) it is possible to define the topology of any topological algebra by a collection of $F$-seminorms, (b) every complete locally uniformly absorbent (complete locally $A$-pseudoconvex) Hausdorff algebra is topologically isomorphic to a projective limit of metrizable locally uniformly absorbent algebras (respectively, $A$-($k$-normed) algebras, where $k\in (0, 1]$ varies), (c) every complete locally idempotent (complete locally $m$-pseudoconvex) Hausdorff algebra is topologically isomorphic to a projective limit of locally idempotent Fréchet algebras (respectively, $k$-Banach algebras, where $k\in (0,1]$ varies), and every $m$-algebra is locally $m$-pseudoconvex. A condition for submultiplicativity of an $F$-seminorm is given.

MSC 2000:: *46H05 General theory of topological algebras
46H20 Structure and classification of topological algebras

Keywords: topological algebra; $F$-seminorm; nonhomogeneous seminorm; locally absorbent algebra; locally idempotent algebra; locally pseudoconvex algebra; locally A-pseudoconvex algebra; locally $m$-pseudoconvex Fréchet algebra; $m$-algebra

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