共查询到20条相似文献,搜索用时 296 毫秒
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Let (m?n) denote the linear space of all m × n complex or real matrices according as = or . Let c=(c1,…,cm)≠0 be such that c1???cm?0. The c-spectral norm of a matrix A?m×n is the quantity . where σ1(A)???σm(A) are the singular values of A. Let d=(d1,…,dm)≠0, where d1???dm?0. We consider the linear isometries between the normed spaces and , and prove that they are dual transformations of the linear operators which map (d) onto (c), where . 相似文献
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Seiya Negami 《Discrete Mathematics》1983,44(2):161-180
A topological generalization of the uniqueness of duals of 3-connected planar graphs will be obtained. A graph G is uniquely embeddable in a surface F if for any two embeddings , , there are an autohomeomorphism h:F → F and an automorphism σ:G → G such that . A graph G is faithfully embedabble in a surface F if there is an embedding such that for any automorphism σ:G → G, there is an autohomeomorphism h:F → F with . Our main theorems state that any 6-connected toroidal graph is uniquelly embeddable in a torus and that any 6-connected toroidal graph with precisely three exceptions is faithfully embeddable in a torus. The proofs are based on a classification of 6-regular torus graphs. 相似文献
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Roger Howe 《Journal of Functional Analysis》1979,32(3):297-303
Let (i, H, E) and (j, K, F) be abstract Wiener spaces and let α be a reasonable norm on E ? F. We are interested in the following problem: is () an abstract Wiener space ? The first thing we do is to prove that the setting of the problem is meaningfull: namely, i ? j is always a continuous one to one map from into . Then we exhibit an example which shows that the answer cannot be positive in full generality. Finally we prove that if F=Lp(X,,λ) for some σ-finite measure λ ? 0 then (X,,λ) is an abstract Wiener space. By-products are some new results on γ-radonifying operators, and new examples of Banach spaces and cross norms for which the answer is affirmative (in particular α = π the projective norm, and F=L1(X,,λ)). 相似文献
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Properties of the graph of the polytope of all n × n nonnegative doubly stochastic matrices are studied. If is a face of which is not a k-dimensional rectangular parallelotope for k ≥ 2, then G() is Hamilton connected. Prime factor decompositions of the graphs of faces of relative to Cartesian product are investigated. In particular, if is a face of , then the number of prime graphs in any prime factor decomposition of G() equals the number of connected components of the neighborhood of any vertex of G(). Distance properties of the graphs of faces of are obtained. Faces of for which G() is a clique of are investigated. 相似文献
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Let K1 and K2 be number fields and . Suppose and are of prime degree p but are not necessarily normal. Let N1 and N2 be the normal closures of K1 and K2 over F, respectively, L = K1K2, N = N1N2, and be a prime divisor of N which divides p and is totally ramified in and . Let be the ramification index of in , be the total ramification number of in , and . Then (K1, K2) is exactly divisible by M, where . 相似文献
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William O Ray 《Journal of Mathematical Analysis and Applications》1984,103(1):162-171
Let {Fr}0?r?p be a family of Banach spaces satisfying, if 0?r1?r2?p, (i)Fr1 ? Fr2; (ii); and (iii) is a convex function. Let G0 be a Banach space and. be a Gâteaux differentiate mapping, and suppose that ′(x)(Fp) is dense in G0. Under appropriate assumptions, the equation (x)=0 has a solution in Fr for 0?r?p. The results extend the Inverse Function Theorem of J. Moser to the class of Gâteaux differentiable operators. 相似文献
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N.J Kalton 《Journal of Functional Analysis》1981,42(3):299-337
We prove a number of results concerning isomorphisms between spaces of the type Lp(X), where X is a separable p-Banach space and 0 < p < 1. Our results imply that the quotient of Lp([0, 1] × [0, 1]) by the subspace of functions depending only on the first variable is not isomorphic to Lp, answering a question of N. T. Peck. More generally if 0 is a sub-σ-algebra of the Borel sets of [0, 1], then , 0) is isomorphic to Lp if and only if Lp([0, 1], B0) is complemented. We also show that Lp has, up to isomorphism, at most one complemented subspace non-isomorphic to Lp and classify completely those spaces X for which . In particular if then or is finite-dimensional. If X has trivial dual and . 相似文献
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Amitai Regev 《Advances in Mathematics》1982,46(2):230-240
An asymptotic formula, involving integrals, is given for certain combinatorial sums. By evaluating a multi-integral it is then found that as n → ∞, the codimensions cn(F2) and the trace codimensions tn(F2) of F2, the 2 × 2 matrices, are asymptotically equal: . 相似文献
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Rahman Younis 《Journal of Functional Analysis》1981,44(3):381-387
The main result of this paper is that if F is a closed subset of the unit circle, then is an M-ideal of . Consequently, if then ? has a closest element in H∞ + LF∞. Furthermore, if is not the dual of any Banach space. 相似文献
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By applying the maximal element theorems on product of G-convex spaces due to the first author, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in G-convex spaces. As applications, some existence theorems of solutions for the system of generalized vector quasiequilibrium problem are established in noncompact product of G-convex spaces. Our results improve and generalize some recent results in the literature to product of G-convex spaces.The authors thank the referees for valuable comments and suggestionsThe research of this author was supported by the National Science Foundation of China, Sichuan Education Department.The research of this author was supported by the National Science Council of the Republic of China. 相似文献
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Karine Sorlin 《Comptes Rendus Mathematique》2002,334(3):179-184
Let G be a connected reductive group defined over and let F be the corresponding Frobenius endomorphism. Let σ be a quasi-central rational automorphism of G. We define in this article Gelfand–Graev representations of the group when σ is unipotent and when it is semi-simple. We show that they have similar properties to Gelfand–Graev representations of the group GF. To cite this article: K Sorlin, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 179–184. 相似文献
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Given two collections F1 and F2 of sets, each member of one intersecting each member of the other, let the collections of latent sets FiL, i = 1, 2, be the sets that are contained in members of Fi but that are not themselves members of Fi. If lower case letters indicate the size of the collections we then have This result is used to prove that a self-intersecting subfamily F of a simplical complex G having the property that any element of F contains s1 or s2 can be no larger than the lesser of the number of elements of G containing s1 and the number containing s2. Certain extensions and a related conjecture of Chvátal are described. 相似文献
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Woody Lichtenstein 《Journal of Functional Analysis》1979,34(3):433-455
For a symmetric space of compact type, the highest-weight vectors for representations of G occurring in become heavily concentrated near certain submanifolds of as the highest weight goes to infinity. This fact is applied to obtain estimates for the spectral measures of the operators qλ = PλqPλ, where is an orthogonal projection onto a G-irreducible summand, and q: G/K → is a continuous function acting on by multiplication. 相似文献
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In this Note we give a generalization of Hardy's theorem for the Dunkl transform on . More precisely, for all a>0, b>0 and p,q∈[1,+∞], we determine the measurable functions f such that and , where are the Lp spaces associated with the Dunkl transform. To cite this article: L. Gallardo, K. Trimèche, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 849–854. 相似文献
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We consider a real semi-simple Lie group G with finite center and a maximal compact sub-group K of G. Let be a Cartan decomposition of G. For x∈G denote ∥x∥ the norm of the -component of x in the Cartan decomposition of G. Let and 1?p,q?∞. In this Note we give necessary and sufficient conditions on such that for all K-bi-invariant measurable function f on G, if ea∥x∥2f∈Lp(G) and then f=0 almost everywhere. To cite this article: S. Ben Farah, K. Mokni, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
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Yuh-Jia Lee 《Journal of Functional Analysis》1982,47(2):153-164
Let (H, B) be an abstract Wiener pair and pt the Wiener measure with variance t. Let a be the class of exponential type analytic functions defined on the complexification [B] of B. For each pair of nonzero complex numbers α, β and f ? a, we define We show that the inverse α,β?1 exists and there exist two nonzero complex numbers α′,β′ such that . Clearly, the Fourier-Wiener transform, the Fourier-Feynman transform, and the Gauss transform are special cases of α,β. Finally, we apply the transform to investigate the existence of solutions for the differential equations associated with the operator c, where c is a nonzero complex number and c is defined by where Δ is the Laplacian and (·, ·) is the pairing. We show that the solutions can be represented as integrals with respect to the Wiener measure. 相似文献
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Alain A. Lewis 《Mathematical Social Sciences》1985,9(3):197-247
Let 1M be a denumerately comprehensive enlargement of a set-theoretic structure sufficient to model R. If F is an internal 1finite subset of 1N such that , we define a class of 1finite cooperative games having the form , where A(F) is the internal algebra of the internal subsets of F, and is a set-function with , , and . If is the space of S-imputations of a game ΓF(1ν) such that , for some , then we prove that contains two nonempty subsets: and , termed the quasi-kernel and S-bargaining set, respectively. Both and are external solution concepts for games of the form ΓF (1ν) and are defined in terms of predicates that are approximate in infinitesimal terms. Furthermore, if L(Θ) is the Loeb space generated by the 1finitely additive measure space 〈F, A(F), UF〉, and if a game ΓF(1ν) has a nonatomic representation on L(Θ) with respect to S-bounded transformations, then the standard part of any element in is Loeb-measurable and belongs to the quasi-kernel of defined in standard terms. 相似文献