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<p>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.</p>

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Continuity of multiplication in projective limit algebras and applications to amenability

  • 期刊论文

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  • 发表日期：

    2025年5月15日

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  • Krzysztof Piszczek

摘要

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.