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We show that for each p∈(0,1] there exists a separable p -Banach space Gp of almost universal disposition, that is, having the following extension property: for each ε>0 and each isometric embedding g:X→Y, where Y is a finite-dimensional p-Banach space and X is a subspace of Gp, there is an ε -isometry f:Y→Gp such that x=f(g(x)) for all x∈X. 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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Roe algebras are C?-algebras built using large scale (or ‘coarse’) aspects of a metric space (X,d). In the special case that X=Γ is a finitely generated group and d is a word metric, the simplest Roe algebra associated to (Γ,d) is isomorphic to the crossed product C?-algebra l∞(Γ)?rΓ. 相似文献
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Denote by gdist(p) the least non-zero number of cells that have to be changed to get a latin square from the table of addition modulo p . A conjecture of Drápal, Cavenagh and Wanless states that there exists c>0 such that gdist(p)?clog(p). In this paper the conjecture is proved for c≈7.21, and as an intermediate result it is shown that an equilateral triangle of side n can be non-trivially dissected into at most 5log2(n) integer-sided equilateral triangles. The paper also presents some evidence which suggests that gdist(p)/log(p)≈3.56 for large values of p. 相似文献
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We prove that for any free ergodic nonsingular nonamenable action Γ?(X,μ) of all Γ in a large class of groups including all hyperbolic groups, the associated group measure space von Neumann algebra L∞(X)?Γ has L∞(X) as its unique Cartan subalgebra, up to unitary conjugacy. This generalizes the probability measure preserving case that was established in Popa and Vaes (in press) [38]. We also prove primeness and indecomposability results for such crossed products, for the corresponding orbit equivalence relations and for arbitrary amalgamated free products M1?BM2 over a subalgebra B of type I. 相似文献
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