un 2 00 3 Dual Banach algebras : Connes - amenability , normal , virtual diagonals , and injectivity of the predual bimodule Volker
نویسنده
چکیده
Let A be a dual Banach algebra with predual A∗ and consider the following assertions: (A) A is Connes-amenable; (B) A has a normal, virtual diagonal; A∗ is an injective A-bimodule. For general A, all that is known is that (B) implies (A) whereas, for von Neumann algebras, (A), (B), and (C) are equivalent. We show that (C) always implies (B) whereas the converse is false. Furthermore, we investigate Connes-amenability and the existence of normal, virtual diagonals for A = WAP(G)∗ and A = B(G), where G is a locally compact group. We give descriptions of these properties in terms of G.
منابع مشابه
Connes - amenability , normal , virtual diagonals , and injectivity of the predual bimodule
Let A be a dual Banach algebra with predual A∗ and consider the following assertions: (A) A is Connes-amenable; (B) A has a normal, virtual diagonal; (C) A∗ is an injective A-bimodule. For general A, all that is known is that (B) implies (A) whereas, for von Neumann algebras, (A), (B), and (C) are equivalent. We show that (C) always implies (B) whereas the converse is false for A = M(G) where G...
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