共查询到20条相似文献,搜索用时 205 毫秒
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H. Movahedi-Lankarani R. Wells 《Journal of Mathematical Analysis and Applications》2003,285(1):299-320
The C1-Weierstrass approximation theorem is proved for any compact subset X of a Hilbert space . The same theorem is also proved for Whitney 1-jets on X when X satisfies the following further condition: There exist finite dimensional linear subspaces such that ?n?1Hn is dense in and πn(X)=X∩Hn for each n?1. Here, is the orthogonal projection. It is also shown that when X is compact convex with and satisfies the above condition, then C1(X) is complete if and only if the C1-Whitney extension theorem holds for X. Finally, for compact subsets of , an extension of the C1-Weierstrass approximation theorem is proved for C1 maps with compact derivatives. 相似文献
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C. Angosto 《Journal of Mathematical Analysis and Applications》2008,343(1):479-491
We establish here some inequalities between distances of pointwise bounded subsets H of RX to the space of real-valued continuous functions C(X) that allow us to examine the quantitative difference between (pointwise) countable compactness and compactness of H relative to C(X). We prove, amongst other things, that if X is a countably K-determined space the worst distance of the pointwise closure of H to C(X) is at most 5 times the worst distance of the sets of cluster points of sequences in H to C(X): here distance refers to the metric of uniform convergence in RX. We study the quantitative behavior of sequences in H approximating points in . As a particular case we obtain the results known about angelicity for these Cp(X) spaces obtained by Orihuela. We indeed prove our results for spaces C(X,Z) (hence for Banach-valued functions) and we give examples that show when our estimates are sharp. 相似文献
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This paper studies the eigenvalues of the p(x)-Laplacian Dirichlet problem
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Salah Mecheri Messaoud Bounkhel 《Journal of Mathematical Analysis and Applications》2003,287(1):51-60
In this paper we characterize the global minimum of an arbitrary function defined on a Banach space, in terms of a new concept of derivatives adapted for our case from a recent work due to D.J. Keckic (J. Operator Theory, submitted for publication). Using these results we establish several new characterizations of the global minimum of the map defined by Fψ(X)=‖ψ(X)‖1, where is a map defined by ψ(X)=S+φ(X) and φ:B(H)→B(H) is a linear map, S∈C1, and . Further, we apply these results to characterize the operators which are orthogonal to the range of elementary operators. 相似文献
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Antoine Derighetti 《Journal of Functional Analysis》2004,215(2):341-365
Let G be a locally compact group and let p∈(1,∞). Let be any of the Banach spaces Cδ,p(G), PFp(G), Mp(G), APp(G), WAPp(G), UCp(G), PMp(G), of convolution operators on Lp(G). It is shown that PFp(G)′ can be isometrically embedded into UCp(G)′. The structure of maximal regular ideals of (and of MAp(G)″, Bp(G)″, Wp(G)″) is studied. Among other things it is shown that every maximal regular left (right, two sided) ideal in is either dense or is the annihilator of a unique element in the spectrum of Ap(G). Minimal ideals of is also studied. It is shown that a left ideal M in is minimal if and only if , where Ψ is either a right annihilator of or is a topologically x-invariant element (for some x∈G). Some results on minimal right ideals are also given. 相似文献
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Kyung Hoon Han 《Journal of Mathematical Analysis and Applications》2007,336(1):569-576
We show that there exists a natural embedding from the tensor product V∗∗⊗W∗∗ of the biduals of operator spaces V and W into the bidual of the injective tensor product of V and W, which is separately weak∗ continuous. From this, we define condition C for operator spaces. 相似文献
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Tuomas P. Hytönen 《Journal of Functional Analysis》2006,234(2):420-463
We establish conditions similar to the Tb theorem of David, Journé and Semmes which guarantee the boundedness of an integral transformation T with L(X)-valued kernel on , where 1<p<∞ and X is a Banach space with the unconditionality property of martingale differences (UMD). 相似文献
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Let H(B) denote the space of all holomorphic functions on the unit ball B of Cn. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. In this paper, we investigate the boundedness and compactness of the generalized composition operator
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Antonio Fernández Fernando Mayoral 《Journal of Mathematical Analysis and Applications》2011,376(1):203-211
For a given measurable space (Ω,Σ), and a vector measure m:Σ→X with values in a Banach space X we consider the spaces of p-power integrable and weakly integrable, respectively, functions with respect to the measure m, Lp(m) and , for 1?p<∞. In this note we describe the real interpolated spaces that we obtain when the K-method is applied to any couple of these spaces. 相似文献
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J.C. Ferrando 《Journal of Mathematical Analysis and Applications》2004,297(2):518-526
We show that metrizability and bounded tightness are actually equivalent for a large class of locally convex spaces including (LF)-spaces, (DF)-spaces, the space of distributions D′(Ω), etc. A consequence of this fact is that for the bounded tightness for the weak topology of X is equivalent to the following one: X is linearly homeomorphic to a subspace of . This nicely supplements very recent results of Cascales and Raja. Moreover, we show that a metric space X is separable if the space Cp(X) has bounded tightness. 相似文献
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For a Tychonoff space X , we denote by Cp(X) and Cc(X) the space of continuous real-valued functions on X equipped with the topology of pointwise convergence and the compact-open topology respectively. Providing a characterization of the Lindelöf Σ-property of X in terms of Cp(X), we extend Okunev?s results by showing that if there exists a surjection from Cp(X) onto Cp(Y) (resp. from Lp(X) onto Lp(Y)) that takes bounded sequences to bounded sequences, then υY is a Lindelöf Σ-space (respectively K-analytic) if υX has this property. In the second part, applying Christensen?s theorem, we extend Pelant?s result by proving that if X is a separable completely metrizable space and Y is first countable, and there is a quotient linear map from Cc(X) onto Cc(Y), then Y is a separable completely metrizable space. We study also a non-separable case, and consider a different approach to the result of J. Baars, J. de Groot, J. Pelant and V. Valov, which is based on the combination of two facts: Complete metrizability is preserved by ?p-equivalence in the class of metric spaces (J. Baars, J. de Groot, J. Pelant). If X is completely metrizable and ?p-equivalent to a first-countable Y, then Y is metrizable (V. Valov). Some additional results are presented. 相似文献
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Chun-Gil Park 《Journal of Mathematical Analysis and Applications》2005,307(2):753-762
It is shown that every almost linear bijection of a unital C∗-algebra A onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all unitaries u∈A, all y∈A, and n=0,1,2,…, and that almost linear continuous bijection of a unital C∗-algebra A of real rank zero onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all , all y∈A, and n=0,1,2,…. Assume that X and Y are left normed modules over a unital C∗-algebra A. It is shown that every surjective isometry , satisfying T(0)=0 and T(ux)=uT(x) for all x∈X and all unitaries u∈A, is an A-linear isomorphism. This is applied to investigate C∗-algebra isomorphisms between unital C∗-algebras. 相似文献
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Let s∈R, τ∈[0,∞), p∈(1,∞) and q∈(1,∞]. In this paper, we introduce a new class of function spaces which unify and generalize the Triebel-Lizorkin spaces with both p∈(1,∞) and p=∞ and Q spaces. By establishing the Carleson measure characterization of Q space, we then determine the relationship between Triebel-Lizorkin spaces and Q spaces, which answers a question posed by Dafni and Xiao in [G. Dafni, J. Xiao, Some new tent spaces and duality theorem for fractional Carleson measures and Qα(Rn), J. Funct. Anal. 208 (2004) 377-422]. Moreover, via the Hausdorff capacity, we introduce a new class of tent spaces and determine their dual spaces , where s∈R, p,q∈[1,∞), max{p,q}>1, , and t′ denotes the conjugate index of t∈(1,∞); as an application of this, we further introduce certain Hardy-Hausdorff spaces and prove that the dual space of is just when p,q∈(1,∞). 相似文献
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Let MC denote a 2 × 2 upper triangular operator matrix of the form , which is acting on the sum of Banach spaces X⊕Y or Hilbert spaces H⊕K. In this paper, the sets and ?C∈B(K,H)σr(MC) are, respectively, characterized completely, where σc(·) denotes the continuous spectrum, σp(·) denotes the point spectrum and σr(·) denotes the residual spectrum. Moreover, some corresponding counterexamples are given. 相似文献
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Marius Junge 《Journal of Functional Analysis》2008,254(5):1373-1409
The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C(K) and ?2 is 2-summing. However, it is shown in [M. Junge, Embedding of the operator space OH and the logarithmic ‘little Grothendieck inequality’, Invent. Math. 161 (2) (2005) 225-286] that the operator space analogue fails. Not every cb-map is completely 2-summing. In this paper, we show an operator space analogue of Maurey's theorem: every cb-map is (q,cb)-summing for any q>2 and hence admits a factorization ‖v(x)‖?c(q)‖vcb‖‖axbq‖ with a,b in the unit ball of the Schatten class S2q. 相似文献