共查询到20条相似文献,搜索用时 31 毫秒
1.
Dong Ni Tan 《数学学报(英文版)》2012,28(6):1197-1208
In this paper we study the isometric extension problem and show that every surjective isometry between the unit spheres of Lp (μ) (1 p ∞, p≠2) and a Banach space E can be extended to a linear isometry from Lp(μ) onto E, which means that if the unit sphere of E is (metrically) isometric to the unit sphere of Lp(μ), then E is linearly isometric to Lp(μ). We also prove that every surjective 1-Lipschitz or anti-1-Lipschitz map between the unit spheres of Lp (μ1, H1) and Lp(μ2,H2) must be an isometry and can be extended to a linear isometry from Lp (μ1,H1) to Lp (μ2,H2), where H1 and H2 are Hilbert spaces. 相似文献
2.
Juan Carlos Ferrando 《Journal of Mathematical Analysis and Applications》2011,380(1):323-326
If (Σ,X) is a measurable space and X a Banach space we investigate the X-inheritance of copies of ?∞ in certain subspaces Δ(Σ,X) of bvca(Σ,X), the Banach space of all X-valued countable additive measures of bounded variation equipped with the variation norm. Among the consequences of our main theorem we get a theorem of J. Mendoza on the X-inheritance of copies of ?∞ in the Bochner space L1(μ,X) and other of the author on the X-inheritance of copies of ?∞ in bvca(Σ,X). 相似文献
3.
We study the numerical index of absolute sums of Banach spaces, giving general conditions which imply that the numerical index of the sum is less or equal than the infimum of the numerical indices of the summands and we provide some examples where the equality holds covering the already known case of c0-, ?1- and ?∞-sums and giving as a new result the case of E-sums where E has the RNP and n(E)=1 (in particular for finite-dimensional E with n(E)=1). We also show that the numerical index of a Banach space Z which contains a dense union of increasing one-complemented subspaces is greater or equal than the limit superior of the numerical indices of those subspaces. Using these results, we give a detailed short proof of the already known fact that, for a fixed p, the numerical indices of all infinite-dimensional Lp(μ)-spaces coincide. 相似文献
4.
For a measurable space (Ω,A), let ?∞(A) be the closure of span{χA:A∈A} in ?∞(Ω). In this paper we show that a sufficient and necessary condition for a real-valued finitely additive measure μ on (Ω,A) to be countably additive is that the corresponding functional ?μ defined by (for x∈?∞(A)) is w*-sequentially continuous. With help of the Yosida-Hewitt decomposition theorem of finitely additive measures, we show consequently that every continuous functional on ?∞(A) can be uniquely decomposed into the ?1-sum of a w*-continuous functional, a purely w*-sequentially continuous functional and a purely (strongly) continuous functional. Moreover, several applications of the results to measure extension are given. 相似文献
5.
In recent papers (cf. [J.L. Arregui, O. Blasco, (p,q)-Summing sequences, J. Math. Anal. Appl. 274 (2002) 812-827; J.L. Arregui, O. Blasco, (p,q)-Summing sequences of operators, Quaest. Math. 26 (2003) 441-452; S. Aywa, J.H. Fourie, On summing multipliers and applications, J. Math. Anal. Appl. 253 (2001) 166-186; J.H. Fourie, I. Röntgen, Banach space sequences and projective tensor products, J. Math. Anal. Appl. 277 (2) (2003) 629-644]) the concept of (p,q)-summing multiplier was considered in both general and special context. It has been shown that some geometric properties of Banach spaces and some classical theorems can be described using spaces of (p,q)-summing multipliers. The present paper is a continuation of this study, whereby multiplier spaces for some classical Banach spaces are considered. The scope of this research is also broadened, by studying other classes of summing multipliers. Let E(X) and F(Y) be two Banach spaces whose elements are sequences of vectors in X and Y, respectively, and which contain the spaces c00(X) and c00(Y) of all X-valued and Y-valued sequences which are eventually zero, respectively. Generally spoken, a sequence of bounded linear operators (un)⊂L(X,Y) is called a multiplier sequence from E(X) to F(Y) if the linear operator from c00(X) into c00(Y) which maps (xi)∈c00(X) onto (unxn)∈c00(Y) is bounded with respect to the norms on E(X) and F(Y), respectively. Several cases where E(X) and F(Y) are different (classical) spaces of sequences, including, for instance, the spaces Rad(X) of almost unconditionally summable sequences in X, are considered. Several examples, properties and relations among spaces of summing multipliers are discussed. Important concepts like R-bounded, semi-R-bounded and weak-R-bounded from recent papers are also considered in this context. 相似文献
6.
The representation of dual spaces of EM(μ,X), owing to its extensive application, is given in this paper. Using the representation, we get the sufficient and necessary conditions of LM(μ,X) possessing drop property, and extend the result of Hudzik and Wang [H. Hudzik, B. Wang, Approximative compactness in Orlicz spaces, J. Approx. Theory 95 (1998) 82-89]. Simultaneously, under some conditions, the weak∗ drop property in LM(μ,X∗) and LM∗(μ,X) is discussed. 相似文献
7.
Hyungjin Huh 《Journal of Mathematical Analysis and Applications》2011,381(2):513-520
We obtain a strong solution in charge critical space L2(R) of the Thirring system and Federbusch equations in one space dimension by using solution representation of the models. The uniqueness is obtained for the solution Ψ∈L∞([0,T];L2(R)∩L4(R)). A decay of local charge and asymptotic behavior of the field can be shown directly. 相似文献
8.
María M. Martínez 《Journal of Mathematical Analysis and Applications》2011,375(1):196-206
Let X be a Banach space and let f∈L∞(R+;X) whose Laplace transform extends analytically to some region containing iR?{0}, possibly having a pole at the origin. In this paper, we give estimates of the decay of certain slight suitable modification of f in terms of the growth of its Laplace transform along the imaginary axis. This technique is applied to obtain decay estimates of smooth orbits of bounded C0-semigroups whose infinitesimal generators have an arbitrary finite boundary spectrum. These results are close to those given recently by C.J.K. Batty and T. Duyckaerts. 相似文献
9.
Dhruba R. Adhikari 《Journal of Mathematical Analysis and Applications》2008,348(1):122-136
Let X be a real reflexive Banach space with dual X∗. Let L:X⊃D(L)→X∗ be densely defined, linear and maximal monotone. Let T:X⊃D(T)→X∗2, with 0∈D(T) and 0∈T(0), be strongly quasibounded and maximal monotone, and C:X⊃D(C)→X∗ bounded, demicontinuous and of type (S+) w.r.t. D(L). A new topological degree theory has been developed for the sum L+T+C. This degree theory is an extension of the Berkovits-Mustonen theory (for T=0) and an improvement of the work of Addou and Mermri (for T:X→X∗2 bounded). Unbounded maximal monotone operators with are strongly quasibounded and may be used with the new degree theory. 相似文献
10.
By a ball-covering B of a Banach space X, we mean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere SX of X; and X is said to have the ball-covering property (BCP) provided it admits a ball-covering by countably many balls. In this note we give a natural example showing that the ball-covering property of a Banach space is not inherited by its subspaces; and we present a sharp quantitative version of the recent Fonf and Zanco renorming result saying that if the dual X∗ of X is w∗ separable, then for every ε>0 there exist a (1+ε)-equivalent norm on X, and an R>0 such that in this new norm SX admits a ball-covering by countably many balls of radius R. Namely, we show that R=R(ε) can be taken arbitrarily close to (1+ε)/ε, and that for X=?1[0,1] the corresponding R cannot be equal to 1/ε. This gives the sharp order of magnitude for R(ε) as ε→0. 相似文献
11.
Xianling Fan 《Journal of Mathematical Analysis and Applications》2008,339(2):1395-1412
We study boundary trace embedding theorems for variable exponent Sobolev space W1,p(⋅)(Ω). Let Ω be an open (bounded or unbounded) domain in RN satisfying strong local Lipschitz condition. Under the hypotheses that p∈L∞(Ω), 1?infp(x)?supp(x)<N, |∇p|∈Lγ(⋅)(Ω), where γ∈L∞(Ω) and infγ(x)>N, we prove that there is a continuous boundary trace embedding W1,p(⋅)(Ω)→Lq(⋅)(∂Ω) provided q(⋅), a measurable function on ∂Ω, satisfies condition for x∈∂Ω. 相似文献
12.
Xiangsheng Xu 《Journal of Mathematical Analysis and Applications》2008,338(1):274-284
In this paper we present some regularity results for solutions to the system −Δu=σ(u)2|∇φ|, div(σ(u)∇φ)=0 in the case where σ(u) is allowed to oscillate between 0 and a positive number as u→∞. In particular, we show that u is locally bounded if σ(u) is bounded below by a suitable exponential function. 相似文献
13.
We construct an example of a Banach space which is not lush, but whose dual space is lush. This example shows that lushness is not equivalent to numerical index one. A characterization of lushness for some quotient spaces of L1(μ) spaces and new results on C-rich subspaces of (scalar- or vector-valued) C(K) spaces are also presented. 相似文献
14.
Marek Balcerzak Katarzyna Dems 《Journal of Mathematical Analysis and Applications》2007,328(1):715-729
Let I⊂P(N) stand for an ideal containing finite sets. We discuss various kinds of statistical convergence and I-convergence for sequences of functions with values in R or in a metric space. For real valued measurable functions defined on a measure space (X,M,μ), we obtain a statistical version of the Egorov theorem (when μ(X)<∞). We show that, in its assertion, equi-statistical convergence on a big set cannot be replaced by uniform statistical convergence. Also, we consider statistical convergence in measure and I-convergence in measure, with some consequences of the Riesz theorem. We prove that outer and inner statistical convergences in measure (for sequences of measurable functions) are equivalent if the measure is finite. 相似文献
15.
We study an elliptic transmission problem in Banach spaces. The problem is considered on the juxtaposition of two intervals, one of which of small length δ, and models physical phenomena in media constituted by two parts with different physical characteristics. We obtain results of existence, uniqueness, maximal regularity and optimal dependence on the parameter δ for Lp solutions of the problem. The main tools of our approach are impedance and admittance operators (i.e. Dirichlet-to-Neumann and Neumann-to-Dirichlet operators) and H∞ functional calculus for sectorial operators in Banach spaces. 相似文献
16.
A biclique B of a simple graph G is the edge-set of a complete bipartite subgraph of G. A biclique cover of G is a collection of bicliques covering the edge-set of G. Given a graph G, we will study the following problem: find the minimum number of bicliques which cover the edge-set of G. This problem will be called the minimum biclique cover problem (MBC). First, we will define the families of independent and dependent sets of the edge-set E(G) of G: F⊆E(G) will be called independent if there exists a biclique B⊆E(G) such that F⊆B, and will be called dependent otherwise. From our study of minimal dependent sets we will derive a 0-1 linear programming formulation of the following problem: find the maximum weighted biclique in a graph. This formulation may have an exponential number of constraints with respect to the number of nodes of G but we will prove that the continuous relaxation of this integer program can be solved in polynomial time. Finally we will also study continuous relaxation methods for the problem (MBC). This research was motivated by an open problem of Fishburn and Hammer. 相似文献
17.
Pradipta Bandyopadhyay Tanmoy Paul 《Journal of Mathematical Analysis and Applications》2010,369(2):525-536
In this paper, we continue our study of ball remotality of subspaces of Banach spaces. In particular, we study the problem in classical sequence spaces c0, c, ?1 and ?∞; and also ball remotality of a Banach space in its bidual. 相似文献
18.
In this note we study the property (w), a variant of Weyl's theorem introduced by Rako?evi?, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T*) coincide whenever T* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w). 相似文献
19.
Markus Weimar 《Journal of Complexity》2012,28(1):59-75
We study the L∞-approximation problem for weighted Banach spaces of smooth d-variate functions, where d can be arbitrarily large. We consider the worst case error for algorithms that use finitely many pieces of information from different classes. Adaptive algorithms are also allowed. For a scale of Banach spaces we prove necessary and sufficient conditions for tractability in the case of product weights. Furthermore, we show the equivalence of weak tractability with the fact that the problem does not suffer from the curse of dimensionality. 相似文献
20.
In this paper, the solution of the nonlinear evolution inclusion problem of the form u′(t)+B(t,u(t))∋f(t) is studied. In this problem, the operators are of type (M) or type (S+), which are different from those of pseudo-monotone operators that had been studied by many authors. At the same time, we study the perturbation problem. In fact, many kinds of evolution equations can be generalized by this problem. The former results are improved and generalized by our conclusions, and we will give more applications. 相似文献