A+ CATEGORY SCIENTIFIC UNIT

Approximate and weak amenability of certain Banach algebras

Volume 197 / 2010

P. Bharucha, R. J. Loy Studia Mathematica 197 (2010), 195-204 MSC: Primary 46H20; Secondary 43A15, 43A32. DOI: 10.4064/sm197-2-5

Abstract

The notions of approximate amenability and weak amenability in Banach algebras are formally stronger than that of approximate weak amenability. We demonstrate an example confirming that approximate weak amenability is indeed actually weaker than either approximate or weak amenability themselves. As a consequence, we examine the (failure of) approximate amenability for $\ell ^{ p}$-sums of finite-dimensional normed algebras.

Authors

  • P. BharuchaMathematical Sciences Institute
    Australian National University
    Canberra, ACT 0200, Australia
    e-mail
  • R. J. LoyMathematical Sciences Institute
    Australian National University
    Canberra, ACT 0200, Australia
    e-mail

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