Approximate amenability of tensor products of Banach algebras

F. Ghahramani*, R. J. Loy

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    Examples constructed by the first author and Charles Read make it clear that many of the hereditary properties of amenability no longer hold for approximate amenability. These and earlier results of the authors also show that the presence of a bounded approximate identity often entails positive results. Here we show that the tensor product of approximately amenable algebras need not be approximately amenable, and investigate conditions under which A and B being approximately amenable implies, or is implied by, A⊗ˆB or A#⊗ˆB# being approximately amenable. Once again, the rôle of having a bounded approximate identity comes to the fore. Our methods also enable us to prove that if A⊗ˆB is amenable, then so are A and B, a result proved by Barry Johnson in 1996 under an additional assumption.

    Original languageEnglish
    Pages (from-to)746-758
    Number of pages13
    JournalJournal of Mathematical Analysis and Applications
    Volume454
    Issue number2
    DOIs
    Publication statusPublished - 15 Oct 2017

    Fingerprint

    Dive into the research topics of 'Approximate amenability of tensor products of Banach algebras'. Together they form a unique fingerprint.

    Cite this