Representation of Topological Algebras by Projective Limit of Fréchet Algebras

Mati Abel

Abstract


It is shown that every topological Hausdorff algebra (in particular, locally pseudoconvex Hausdorff algebra) $A$ with jointly continuous multiplication is topologically isomorphic to a dense subalgebra of the projective limit of Fréchet (respectively, locally pseudoconvex Fréchet) algebras. In case, when $A$ is complete, $A$ and this projective limit of Fréchet (respectively, locally pseudoconvex Fréchet) algebras are topologically isomorphic. A partly new proof for these results from [11] are given.

Keywords


Topological algebra; Locally pseudoconvex algebra; Fréchet algebra; $F$-seminorm; Projective limit of topological algebras

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DOI: http://dx.doi.org/10.26713%2Fcma.v3i1.140

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eISSN 0975-8607; pISSN 0976-5905