Approximate amenability of tensor products of Banach algebras

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:454

Article

Ghahramani, F.¹  Loy, R. J.² 

[1] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

[2] Australian Natl Univ, Math Sci Inst, Bldg 27,Union Lane, Canberra, ACT 2601, Australia

关键词: Approximately amenable Banach algebra;    Amenable Banach algebra;    Tensor product;    Approximate identity;   

DOI  :  10.1016/j.jmaa.2017.05.018

来源: Elsevier

【 摘 要 】

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 (circle times) over capB or A#(circle times) over capB# being approximately amenable. Once again, the role of having a bounded approximate identity comes to the fore. Our methods also enable us to prove that if A B is amenable, then so are A and B, a result proved by Barry Johnson in 1996 under an additional assumption. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free