Abstract
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\break 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. Condition for submultiplicativity of $F$-seminorm is given.
Citation
Mati Abel. "Representations of topological algebras by projective limits." Ann. Funct. Anal. 1 (1) 144 - 157, 2010. https://doi.org/10.15352/afa/1399901000
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