Relative amenability and the non-amenability of B(l1)

Journal of the Australian Mathematical Society

C. J. Read¹ 

关键词: primary 46J20;    46H10;    secondary 46H20;    13A05;    13G05;    46J05;   

DOI  :  10.1017/S1446788700014038

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

In this paper we begin with a short, direct proof that the Banach algebra B(l1) is not amenable. We continue by showing that various direct sums of matrix algebras are not amenable either, for example the direct sum of the finite dimensional algebrasis no amenable for 1 ≤ p ≤ ∞, p ≠ 2. Our method of proof naturally involves free group algebras, (by which we mean certain subalgebras of B(X) for some space X with symmetric basis—not necessarily X = l2) and we introduce the notion of ‘relative amenability’ of these algebras.

【 授权许可】

Unknown