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Let K be a hypergroup with a Haar measure. The purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of L∞(K) and C0(K), the class of left translation invariant w?-subalgebras of L∞(K) and finally the class of non-zero left translation invariant C?-subalgebras of C0(K) in the hypergroup context with the goal of finding some relations between these function spaces. Among other results, we construct two correspondences: one, between closed Weil subhypergroups and certain left translation invariant w?-subalgebras of L∞(K), and another, between compact subhypergroups and a specific subclass of the class of left translation invariant C?-subalgebras of C0(K). By the help of these two characterizations, we extract some results about invariant complemented subspaces of L∞(K) and C0(K). 相似文献
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Let G be a countable discrete group with an orthogonal representation α on a real Hilbert space H . We prove Lp Poincaré inequalities for the group measure space L∞(ΩH,γ)?G, where both the group action and the Gaussian measure space (ΩH,γ) are associated with the representation α . The idea of proof comes from Pisier?s method on the boundedness of Riesz transform and Lust-Piquard?s work on spin systems. Then we deduce a transportation type inequality from the Lp Poincaré inequalities in the general noncommutative setting. This inequality is sharp up to a constant (in the Gaussian setting). Several applications are given, including Wiener/Rademacher chaos estimation and new examples of Rieffel?s compact quantum metric spaces. 相似文献
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We study the interplay of C?-dynamics and K -theory. Notions of chain recurrence for transformations groups (X,Γ) and MF actions for non-commutative C?-dynamical systems (A,Γ,α) are translated into K-theoretical language, where purely algebraic conditions are shown to be necessary and sufficient for a reduced crossed product to admit norm microstates. We are particularly interested in actions of free groups on AF algebras, in which case we prove that a K-theoretic coboundary condition determines whether or not the reduced crossed product is a matricial field (MF) algebra. One upshot is the equivalence of stable finiteness and being MF for these reduced crossed product algebras. 相似文献
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We show that an n-homogeneous polynomial P on the Fourier algebra A(G) of a locally compact group G can be represented in the form P(f)=〈T,fn〉(f∈A(G)) for some T in the group von Neumann algebra VN(G) of G if and only if it is orthogonally additive and completely bounded. 相似文献
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Mohamed Ali Toumi 《Expositiones Mathematicae》2010,28(3):269-275
Let A be an Archimedean f -algebra and let N(A) be the set of all nilpotent elements of A. Colville et al. [4] proved that a positive linear map d:A→A is a derivation if and only if d(A)⊂N(A) and d(A2)={0}, where A2 is the set of all products ab in A. 相似文献
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In this paper, the approximation characteristic of a diagonal matrix in probabilistic and average case settings is investigated. And the asymptotic degree of the probabilistic linear (n,δ)-width and p-average linear n-width of diagonal matrix M are determined. 相似文献
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We utilize the classical hypercircle method and the lowest-order Raviart–Thomas H(div) element to obtain a posteriori error estimates of the P1 finite element solutions for 2D Poisson's equation. A few other estimation methods are also discussed for comparison. We give some theoretical and numerical results to see the effectiveness of the methods. 相似文献
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