Continuity of multiplication in projective limit algebras and applications to amenability

We study Köthe PDF-algebras. Using two (different yet natural) definitions of multiplication we obtain a wide class of natural algebras with either discontinuous or continuous multiplication. In this last case, we are able to fully characterize amenable Köthe PDF-algebras in terms of the defining Kö...

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Bibliographic Details
Published inAnnals of functional analysis Vol. 16; no. 3
Main Author Piszczek, Krzysztof
Format Journal Article
LanguageEnglish
Published 01.07.2025
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ISSN2639-7390
2008-8752
DOI10.1007/s43034-025-00431-7

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Summary:We study Köthe PDF-algebras. Using two (different yet natural) definitions of multiplication we obtain a wide class of natural algebras with either discontinuous or continuous multiplication. In this last case, we are able to fully characterize amenable Köthe PDF-algebras in terms of the defining Köthe matrix. This characterization shows an interesting and unexpected relation between algebraic and topological structures of amenable Köthe PDF-algebras.
ISSN:2639-7390
2008-8752
DOI:10.1007/s43034-025-00431-7