共查询到20条相似文献,搜索用时 531 毫秒
1.
Ondej F.K. Kalenda 《Journal of Mathematical Analysis and Applications》2009,350(2):464-484
We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L1 spaces, Banach lattices and noncommutative L1 spaces. 相似文献
2.
In this paper, we will study the isometric extension problem for L1-spaces and prove that every surjective isometry from the unit sphere of L1(μ) onto that of a Banach space E can be extended to a linear surjective isometry from L1(μ) onto E. Moreover, we introduce the approximate isometric extension problem and show that, if E and F are Banach spaces and E satisfies the property (m) (special cases are L∞(Γ), C0(Ω) and L∞(μ)), then every bijective ?-isometry between the unit spheres of E and F can be extended to a bijective 5?-isometry between their closed unit balls. At last, we will give an example to show that the surjectivity assumption cannot be omitted. Using this, we solve the non-surjective isometric extension problem in the negative. 相似文献
3.
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
4.
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
5.
We shall present several Hanner type inequalities with a weight constant and characterize 2-uniformly smooth and 2-uniformly convex Banach spaces with these inequalities. p-Uniformly smooth and q-uniformly convex Banach spaces will be also characterized with another Hanner type inequalities with a weight in the other side term. The best value of the weight in these inequalities will be determined for Lp spaces. Also we shall present a duality theorem between these inequalities in a generalized form. 相似文献
6.
Zongliang Sun 《Journal of Mathematical Analysis and Applications》2011,373(1):287-296
We make some comparisons concerning the induced infinitesimal Kobayashi metric, the induced Siegel metric, the L2 Bergman metric, the Teichmüller metric and the Weil-Petersson metric on the Teichmüller space of a compact Riemann surface of genus g?2. As a consequence, among others, we show that the moduli space has finite volume with respect to the L2 Bergman metric. This answers a question raised by Nag in 1989. 相似文献
7.
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
8.
Miguel Sama 《Journal of Mathematical Analysis and Applications》2010,372(1):262-272
This paper underlines the role of directional compactness in the scalarization of graphical derivatives of set-valued maps taking values in infinite-dimensional spaces. Two main theorems are given. The first one states the equivalence of contingent epiderivatives and τw-contingent epiderivatives for directionally compact maps. The second main result proves a variational characterization for the contingent epiderivative of stable and directionally compact maps taking values in general image spaces, extending known results in finite-dimensional and reflexive Banach spaces. The hypotheses given are minimal as is shown by means of several examples. Connections of these theorems with other results of the literature are also provided. 相似文献
9.
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
10.
Chi-Wai Leung 《Journal of Mathematical Analysis and Applications》2006,322(2):699-711
In this article, we define a natural Banach ∗-algebra for a C∗-dynamical system (A,G,α) which is slightly bigger than L1(G;A) (they are the same if A is finite-dimensional). We will show that this algebra is ∗-regular if G has polynomial growth. The main result in this article extends the two main results in [C.W. Leung, C.K. Ng, Functional calculus and ∗-regularity of a class of Banach algebras, Proc. Amer. Math. Soc., in press]. 相似文献
11.
F. Rambla 《Journal of Mathematical Analysis and Applications》2006,317(2):659-667
We prove that if the one-point compactification of a locally compact, noncompact Hausdorff space L is the topological space called pseudoarc, then C0(L,C) is almost transitive. We also obtain two necessary conditions on a metrizable locally compact Hausdorff space L for C0(L) being almost transitive. 相似文献
12.
J.C. Ferrando 《Journal of Mathematical Analysis and Applications》2006,324(2):862-881
Valdivia invented a nondistinguished Fréchet space whose weak bidual is quasi-Suslin but not K-analytic. We prove that Grothendieck/Köthe's original nondistinguished Fréchet space serves the same purpose. Indeed, a Fréchet space is distinguished if and only if its strong dual has countable tightness, a corollary to the fact that a (DF)-space is quasibarrelled if and only if its tightness is countable. This answers a Cascales/K?kol/Saxon question and leads to a rich supply of (DF)-spaces whose weak duals are quasi-Suslin but not K-analytic, including the spaces Cc(κ) for κ a cardinal of uncountable cofinality. Our level of generality rises above (DF)- or even dual metric spaces to Cascales/Orihuela's class G. The small cardinals b and d invite a novel analysis of the Grothendieck/Köthe example, and are useful throughout. 相似文献
13.
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
14.
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
15.
T.L. Miller V.G. Miller M.M. Neumann 《Journal of Mathematical Analysis and Applications》2005,301(1):32-51
We adapt recent results of Albrecht and Ricker to obtain conditions under which growth constraints on the left resolvent of a Banach space operator are preserved under suitable perturbations. As an application, we establish Bishop's property (β) for certain generalized Cesàro operators on the classical Hardy spaces Hp, 1<p<∞. Our methods also apply to unilateral weighted shifts whose weight sequence converges sufficiently rapidly as well as to perturbations of restrictions of a class of generalized scalar operators. 相似文献
16.
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
17.
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
18.
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
19.
Ond?ej Kurka 《Journal of Mathematical Analysis and Applications》2010,371(2):425-435
We study binormality, a separation property of the norm and weak topologies of a Banach space. We show that every Banach space which belongs to a P-class is binormal. We also show that the asplundness of a Banach space is equivalent to a related separation property of its dual space. 相似文献
20.
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