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For a space X denote by Cb(X) the Banach algebra of all continuous bounded scalar-valued functions on X and denote by C0(X) the set of all elements in Cb(X) which vanish at infinity. 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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Let X be a completely regular Hausdorff space and Cb(X) be the Banach space of all real-valued bounded continuous functions on X, endowed with the uniform norm. It is shown that every weakly compact operator T from Cb(X) to a quasicomplete locally convex Hausdorff space E can be uniquely decomposed as T=T1+T2+T3+T4, where Tk:Cb(X)→E(k=1,2,3,4) are weakly compact operators, and T1 is tight, T2 is purely τ -additive, T3 is purely σ -additive and T4 is purely finitely additive. Moreover, we derive a generalized Yosida–Hewitt decomposition for E-valued strongly bounded regular Baire measures. 相似文献
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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 K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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For any closed subset F of [1,∞] which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space X with a 1-unconditional basis is constructed so that in each block subspace Y of X , ?p is finitely block represented in Y if and only if p∈F. In particular, this solves the question as to whether the stabilized Krivine set for a Banach space had to be connected. We also prove that for every infinite dimensional subspace Y of X there is a dense subset G of F such that the spreading models admitted by Y are exactly the ?p for p∈G. 相似文献
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Guang-Xin Huang Feng Yin Ke Guo 《Journal of Computational and Applied Mathematics》2008,217(1):259-267
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It is proved that for each prime field GF(p), there is an integer np such that a 4-connected matroid has at most np inequivalent representations over GF(p). We also prove a stronger theorem that obtains the same conclusion for matroids satisfying a connectivity condition, intermediate between 3-connectivity and 4-connectivity that we term “k-coherence”. 相似文献
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Let G be a simple connected graph of order n with degree sequence d1,d2,…,dn in non-increasing order. The signless Laplacian spectral radius ρ(Q(G)) of G is the largest eigenvalue of its signless Laplacian matrix Q(G). In this paper, we give a sharp upper bound on the signless Laplacian spectral radius ρ(Q(G)) in terms of di, which improves and generalizes some known results. 相似文献