2009/08/25 by G. H. Esslamzadeh, Esslamzadeh, G. H., B. Shojaee +1
Mathematics · #46H20 #46H25 #46H35 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46H20 #msc:46H25 #msc:46H35
paper · pdf · doi:10.48550/arxiv.0908.3566
19 pages. This is a totally restructured version of the former one which includes some further results on measure algebras and von Neumann algebras
arxiv created 2011/01/24 · arxiv updated 2011/01/25
We introduce the notions of approximate Connes-amenability and approximate strong Connes-amenability for dual Banach algebras. Then we characterize these two types of algebras in terms of approximate normal virtual diagonals and approximate σWC-virtual diagonals. We investigate these properties for von Neumann algebras and measure algebras of locally compact groups. In particular we show that a von Neumann algebra is approximately Connes-amenable if and only if it has an approximate normal virtual diagonal. This is the ``approximate'' analog of the main result of Effros in [E. G. Effros, Amenability and virtual diagonals for von Neumann algebras, J. Funct. Anal. 78 (1988), 137-153]. We show that in general the concepts of approximate Connes-ameanbility and Connes-ameanbility are distinct, but for measure algebras these two concepts coincide. Moreover cases where approximate Connes-amenability of \A** implies approximate Connes-amenability or approximate amenability of \A are also discussed.