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1.
Following results of Bourgain and Gorelik we show that the spaces
p
, 1<p<, as well as some related spaces have the following uniqueness property: IfX is a Banach space uniformly homeomorphic to one of these spaces then it is linearly isomorphic to the same space. We also prove that if aC(K) space is uniformly homeomorphic toc
0, then it is isomorphic toc
0. We show also that there are Banach spaces which are uniformly homeomorphic to exactly 2 isomorphically distinct spaces.Dedicated to the memory of E. GorelikThe first author was an Erna and Jacob Michael Visiting Professor, The Weizmann Institute, 1994; and partially supported by NSF DMS 93-06376 and the U.S.-Israel Binational Science Foundation. The second and third authors were participants in the Workshop in Linear Analysis and Probability, Texas A&M University; and were partially supported by the U.S.-Israel Binational Science Foundation. 相似文献
2.
Chen ShuTao Hudzik Henryk Kowalewski Wojciech Wang YuWen Wisła Marek 《中国科学A辑(英文版)》2008,51(2):293-303
First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T~ ,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y. 相似文献
3.
Loukas GRAFAKOS 《中国科学A辑(英文版)》2008,51(12):2253-2284
Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a dimension n. For α∈ (0, ∞) denote by Hαp(X ), Hdp(X ), and H?,p(X ) the corresponding Hardy spaces on X defined by the nontangential maximal function, the dyadic maximal function and the grand maximal function, respectively. Using a new inhomogeneous Calder′on reproducing formula, it is shown that all these Hardy spaces coincide with Lp(X ) when p ∈ (1, ∞] a... 相似文献
4.
On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces 总被引:6,自引:0,他引:6
Ronald E. Bruck 《Israel Journal of Mathematics》1981,38(4):304-314
We prove that ifC is a bounded closed convex subset of a uniformly convex Banach space,T:C→C is a nonlinear contraction, andS
n
=(I+T+…+T
n−1
)/n, then lim
n
‖S
n
(x)−TS
n
(x)‖=0 uniformly inx inC. T also satisfies an inequality analogous to Zarantonello’s Hilbert space inequality. which permits the study of the structure
of the weak ω-limit set of an orbit. These results are valid forB-convex spaces if some additional condition is imposed on the mapping.
Partially supported by NSF Grant MCS-7802305A01. 相似文献
5.
Huang Jianfeng Wang Yuanheng 《高校应用数学学报(英文版)》2007,22(3):311-315
This paper studies the convergence of the sequence defined by x0∈C,xn 1=αnu (1-αn)Txn,n=0,1,2,…, where 0 ≤αn ≤ 1, limn→∞αn = 0, ∑∞n=0 αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results. 相似文献
6.
Shixin Gan 《数学学报(英文版)》1999,15(2):187-196
In this paper, we prove that under theF
4 conditions, anyL log+
L bounded two-parameter Banach spece valued martingale converges almost surely to an integrable Banach space valued random
variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains
true if theF
4 condition is replaced by the weaker localF
4 condition.
Project supported by the National Natural Science Foundation of China and the State Education Commission Ph. D. Station Foundation 相似文献
7.
N. J. Kalton 《Israel Journal of Mathematics》1985,52(4):305-319
Our main result in this paper is that a Banach spaceX embeds intoL
1 if and only ifl
1(X) embeds intoL
0; more generally if 1≦p<2,X embeds intoL
p if and only ifl
p(X) embeds intoL
0.
Research supported by NSF grant MCS-8301099. 相似文献
8.
We classify several classes of the subspaces of Banach spaces X for which there is a bounded linear operator from a Hilbert space onto a dense subset in X. Dually, we provide optimal affine homeomorphisms from weak star dual unit balls onto weakly compact sets in Hilbert spaces or in c0(Γ) spaces in their weak topology. The existence of such embeddings is characterized by the existence of certain uniformly Gâteaux smooth norms. 相似文献
9.
Jing-shi XU Department of Mathematics Hunan Normal University Changsha China 《中国科学A辑(英文版)》2007,50(3):361-376
The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RBMO(μ) functions of Tolsa with non-doubling measures is obtained, provided that‖μ‖=∞and multilinear singular integrals are bounded from L1(μ)×L1(μ)to L1/2,∞(μ). 相似文献
10.
Let X be a Banach space. We show that each m : ? \ {0} → L (X ) satisfying the Mikhlin condition supx ≠0(‖m (x )‖ + ‖xm ′(x )‖) < ∞ defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is isomorphic to a Hilbert space; each bounded measurable function m : ? → L (X ) having a uniformly bounded variation on dyadic intervals defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is a UMD space. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
N. J. Kalton 《Israel Journal of Mathematics》2013,194(1):151-182
We give several examples of separable Banach spaces which are nonisomorphic but uniformly homeomorphic. For example, we show that for every 1 < p ≠ 2 < ∞ there are two uniformly homeomorphic subspaces (respectively, quotients) of ? p which are not linearly isomorphic; similarly c 0 has two uniformly homeomorphic subspaces which are not isomorphic. We also give an example of two non-isomorphic separable L ∞-spaces which are coarsely homeomorphic (i.e. have Lipschitz equivalent nets). 相似文献
12.
We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p > 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1<p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results. 相似文献
13.
By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings. 相似文献
14.
Anthony Weston 《Israel Journal of Mathematics》1993,83(3):375-380
in this paper we prove that for 0<p, q≤1 the real F-spacesL
q[0, 1] and ℓ
p
are not uniformly homeomorphic. The particular casep=q=1 is due to Enflo and our work is motivated by his.
Partially supported by NSF grant #DMS-9104040. The author would like to dedicate this paper to Nancy and Bernie Weston on
the occasion of their 40th wedding anniversary. 相似文献
15.
Assume that the unit spheres of Banach spaces X and Y are uniformly homeomorphic.Then we prove that all unit spheres of the Lebesgue–Bochner function spaces L_p(μ, X) and L_q(μ, Y)are mutually uniformly homeomorphic where 1 ≤ p, q ∞. As its application, we show that if a Banach space X has Property H introduced by Kasparov and Yu, then the space L_p(μ, X), 1 ≤ p ∞,also has Property H. 相似文献
16.
Johnson William B. Lindenstrauss Joram Schechtman Gideon 《Israel Journal of Mathematics》1986,54(2):129-138
It is proved that ifY ⊂X are metric spaces withY havingn≧2 points then any mapf fromY into a Banach spaceZ can be extended to a map
fromX intoZ so that
wherec is an absolute constant. A related result is obtained for the case whereX is assumed to be a finite-dimensional normed space andY is an arbitrary subset ofX.
Supported in part by US-Israel Binational Science Foundation and by NSF MCS-7903042.
Supported in part by NSF MCS-8102714. 相似文献
17.
We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically
embeds. This solves problems raised by J. Bourgain [B] in 1980 and by W. B. Johnson in 1977 [Jo]. We also give intrinsic characterizations
of separable reflexive Banach spaces which embed into a reflexive space with a block q-Hilbertian and/or a block p-Besselian finite dimensional decomposition.
Dedicated to the memory of V. I. Gurarii
Research supported by the National Science Foundation. 相似文献
18.
It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL
p
(B)∩h(B) onto Bergman spaceL
p
(B) ∩
H(B) for 0p 1 ands (p1-1)(n+1). As an application it is shown that the Gleason’s problem can be solved in Bergman space LP(B)∩H(B) for 0p 1.
Project supported by the National Natural Science Foundation of China (Grant No. 19871081) and the Doctoral Program Foundation
of the State Education Commission of China. 相似文献
19.
Summary Distances between measures on IR
d are determined from distances between their 1-dimensional projections. The method employed involves considering the 1-dimensional projections to be the Radon transform of the measures. Crucial to the main theorem is a continuity result for the inverse Radon transform. Focus is restricted to the Prohorov, dual bounded Lipschitz and d
k metrics which metrize weak convergence of probability measures. These metrics are related to each other and to the Sobolev norms. The d
k results extend from measures to generalized functions.Partially supported by NSF Grant No. MCS-81-01895Partially supported by NSF Grant No. MCS-82-01627 and support from the Mellon Foundation 相似文献
20.
The existence of special kind of winning strategies in the Banach-Mazur game in a completely regular topological spaceX is shown to be equivalent to generic stability properties of optimization problems generated by the continuous bounded real-valued functions inX.Research partially supported by the National Foundation for Scientific Research at the Bulgarian Ministry of Education and Science under Grant Number MM-408/94. 相似文献