CONNES-AMENABILITY AND NORMAL, VIRTUAL DIAGONALS FOR MEASURE ALGEBRAS I
نویسندگان
چکیده
منابع مشابه
Connes-amenability and normal, virtual diagonals for measure algebras, II
We prove that the following are equivalent for a locally compact group G: (i) G is amenable; (ii) M(G) is Connes-amenable; (iii) M(G) has a normal, virtual diagonal.
متن کاملConnes-amenability and normal, virtual diagonals for measure algebras
We prove that the measure algebra M(G) of a locally compact group G is Connesamenable if and only if G is amenable.
متن کاملun 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...
متن کامل$sigma$-Connes Amenability and Pseudo-(Connes) Amenability of Beurling Algebras
In this paper, pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2003
ISSN: 0024-6107,1469-7750
DOI: 10.1112/s0024610703004125