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2 results

  • AN ALGEBRA WHOSE SUBALGEBRAS ARE CHARACTERIZED BY DENSITY

  • ALESSANDRO VIGNATI
  • Journal:
    The Journal of Symbolic Logic / Volume 80 / Issue 3 / September 2015
    Published online by Cambridge University Press:
    22 July 2015, pp. 1066-1074
    Print publication:
    September 2015

  • We refine a construction of Choi, Farah, and Ozawa to build a nonseparable amenable operator algebra ${\rm {\cal A}}$ ⊆ ℓ∞ (M2) whose nonseparable subalgebras, including ${\rm {\cal A}}$, are not isomorphic to a C*-algebra. This is done using a Luzin gap and a uniformly bounded group representation.

    Next, we study additional properties of ${\rm {\cal A}}$ and of its separable subalgebras, related to the Kadison Kastler metric.

  • WEAK FORMS OF AMENABILITY FOR BANACH ALGEBRAS

  • Part of
  • H. SAMEA
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 85 / Issue 3 / June 2012
    Published online by Cambridge University Press:
    30 November 2011, pp. 509-517
    Print publication:
    June 2012
    • Article
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  • In this paper, the amenability and approximate amenability of weighted ℓp-direct sums of Banach algebras with unit, where 1≤p<∞, are completely characterized. Applications to compact groups and hypergroups are given.