Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule
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چکیده
منابع مشابه
un 2 00 3 Dual Banach algebras : Connes - amenability , normal , virtual diagonals , and injectivity of the predual bimodule Volker
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 investi...
متن کاملConnes - 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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Generalizing the notion of character amenability for Banach algebras, we study the concept of $varphi$-Connes amenability of a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$, where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$ that lies in $mathcal{A}_*$. Several characterizations of $varphi$-Connes amenability are given. We also prove that the follo...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2004
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-14452