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Claire Anantharaman-Delaroche 《Mathematische Annalen》1987,279(2):297-315
Sans résumé 相似文献
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Claire Anantharaman-Delaroche 《Transactions of the American Mathematical Society》2002,354(10):4153-4178
We study the relations between amenability (resp. amenability at infinity) of -dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.
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The close relationship between the notions of positive formsand representations for a C*-algebra A is one of the most basicfacts in the subject. In particular the weak containment ofrepresentations is well understood in terms of positive forms:given a representation of A in a Hilbert space H and a positiveform on A, its associated representation is weakly containedin (that is, ker ker ) if and only if belongs to the weak*closure of the cone of all finite sums of coefficients of .Among the results on the subject, let us recall the followingones. Suppose that A is concretely represented in H. Then everypositive form on A is the weak* limit of forms of the typex ki=1 i, xi with the i in H; moreover if A is a von Neumannsubalgebra of (H) and is normal, there exists a sequence (i)i 1 in H such that (x) = i 1 i, xi for all x. 相似文献
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Claire Anantharaman-Delaroche 《Probability Theory and Related Fields》2006,135(4):520-546
We extend in a noncommutative setting the individual ergodic theorem of Nevo and Stein concerning measure preserving actions
of free groups and averages on spheres s2n of even radius. Here we study state preserving actions of free groups on a von Neumann algebra A and the behaviour of (s2n(x)) for x in noncommutative spaces Lp(A). For the Cesàro means this problem was solved by Walker. Our approach is based on ideas of Bufetov. We prove a noncommutative version of Rota ``Alternierende
Verfahren' theorem. To this end, we introduce specific dilations of the powers of some noncommutative Markov operators. 相似文献
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Claire Anantharaman-Delaroche 《Israel Journal of Mathematics》2003,137(1):1-33
We show that a measuredG-space (X, μ), whereG is a locally compact group, is amenable in the sense of Zimmer if and only if the following two conditions are satisfied:
the associated unitary representationπ
X ofG intoL
2(X, μ) is weakly contained into the regular representationλ
G and there exists aG-equivariant norm one projection fromL∞(X×X) ontoL∞(X). We give examples of ergodic discrete group actions which are not amenable, althoughπ
X is weakly contained intoλ
G. 相似文献
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