共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
For X a compact Hausdorff topological space and F a strictly convex and reflexive Banach space we characterize the surjective isometries of certain subspaces of C(X, F). It follows from this characterization that surjective isometries on spaces of vector valued Lipschitz functions equipped with a p-norm are also weighted composition operators. 相似文献
3.
E. Mayer-Wolf 《Israel Journal of Mathematics》1981,38(1-2):58-74
The Banach spaces Lip
a
(S, Δ), lip
a
(S, Δ), Lip
a
(S, Δ;s
0) and lip
a
(S, Δ;s
0) of Lipschitz functions are defined. We shall identify the extreme points of the unit balls in their corresponding dual spaces
and make use of them to present a complete characterization of the isometries between these function spaces.
This paper is a part of the author’s M.Sc. thesis which was prepared under the guidance of Dr. Y. Benyamini. 相似文献
4.
5.
《Mathematische Nachrichten》2018,291(11-12):1899-1907
In this article, we describe isometries over the Lipschitz spaces under certain conditions. Indeed, we provide a unified proof for the main results of 3 and 5 in a more general setting. Finally, we extend our results for some other functions spaces like the space of vector‐valued little Lipschitz maps and pointwise Lipschitz maps. 相似文献
6.
Fernanda Botelho 《Linear algebra and its applications》2010,432(12):3337-3342
In this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued Lipschitz functions. We also derive a representation for the generalized bi-circular projections on these spaces. 相似文献
7.
We generalize the celebrated theorem of Stein on the maximal operator of a sequence of translation invariant operators, from the scalar case to vector valued functions. 相似文献
8.
For any weighted space HV(G) of holomorphic functions on an open set G ? ?Nwith a topology stronger than that of uniform convergence on the compact sets and for any quasibarrelled space E we prove the topological isomorphism $HV(G,E_{b}^{\prime})={\cal L}_b(E,HV(G))$ and derive a similar, more complicated isomorphism for weighted spaces of continuous functions. This generalizes results of [3], [7] and [6] and should be compared with the ∈-product representations for the corresponding spaces of functions with o-growth conditions. At the end we also show the topological isomorphism HV1(G1, HV2(G2)) = H (V1 ? V2)(G1 × G2). 相似文献
9.
10.
Giovanni Emmanuele 《Rendiconti del Circolo Matematico di Palermo》1991,40(3):438-441
We prove thatE(X) is a Gelfand-Phillips space if and only ifE andX are. 相似文献
11.
E. Durand-Cartagena 《Journal of Mathematical Analysis and Applications》2010,363(2):525-548
For a metric space X, we study the space D∞(X) of bounded functions on X whose pointwise Lipschitz constant is uniformly bounded. D∞(X) is compared with the space LIP∞(X) of bounded Lipschitz functions on X, in terms of different properties regarding the geometry of X. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare D∞(X) with the Newtonian-Sobolev space N1,∞(X). In particular, if X supports a doubling measure and satisfies a local Poincaré inequality, we obtain that D∞(X)=N1,∞(X). 相似文献
12.
In this paper, we prove some basic results concerning the best approximation of vector-valued functions by algebraic and trigonometric
polynomials with coefficients in normed spaces, called generalized polynomials. Thus we obtain direct and inverse theorems
for the best approximation by generalized polynomials and results concerning the existence (and uniqueness) of best approximation
generalized polynomials.
This paper was written during the 2005 Spring Semester when the second author (S.G. Gal) was a Visiting Professor at the Department
of Mathematical Sciences, The University of Memphis, TN, USA.
Mathematics Subject Classification (2000) 41A65, 41A17, 41A27 相似文献
13.
Neil E. Gretsky 《Annali di Matematica Pura ed Applicata》1974,101(1):337-354
Summary The notation of Gramian matrix is generalized to operators between function spaces and then used to provide an operator-valued
inner product between pairs of Hilbert space-valued Banach function spaces. In this context projection operators, Schwarz's
inequality, and orthonormal series are discussed.
Entrata in Redazione il 26 marzo 1973. 相似文献
14.
15.
We characterize the surjective isometries of a class of analytic functions on the disk which include the Analytic Besov spaceB
p
and the Dirichlet spaceD
p
. In the case ofB
p
we are able to determine the form of all linear isometries on this space. The isometries for these spaces are finite rank perturbations of integral operators. This is in contrast with the classical results for the Hardy and Bergman spaces where the isometries are represented as weighted compositions induced by inner functions or automorphisms of the disk. 相似文献
16.
《Indagationes Mathematicae (Proceedings)》1987,90(1):41-50
Let C(X,E) be the space of all continuous functions from an ultraregular space X to a non-Archimedean locally convex space E. Necessary and/or sufficient conditions are given so that C(X,E), with the topology of uniform convergence on compact sets or with the topology of simple convergence, is bornological or c-ultrabornological. 相似文献
17.
18.
René T. Rau 《Semigroup Forum》1994,48(1):107-118
In [13] we characterized exponentially dichotomic evolution operators (U(t,s))
t,s∈ℝ on a Banach spaceE in terms of the spectrum of an associatedC
0-group on anE-valued function space. In this paper we investigate the more general case of hyperbolic evolution families (U(t,s))
t≥s,s∈ℝ and derive a spectral characterization through an associatedC
0-semigroup. We then apply the results to periodic initial value problems and show that the semigroup can be interpreted as
a generalized monodromy operator. Furthermore we briefly discuss the spectral properties of aC
0-semigroup associated with an evolution family (U(t, s))
t
≥s≥0.
Supported by the Deutsche Forschungsgemeinschaft 相似文献
19.
20.
ZHANG HAITAO 《高校应用数学学报(英文版)》1994,9(3):315-318
ANOTEONVECTORVALUEDANALYTICFUNCTIONS¥ZHANGHAITAO(DepartmentofMathematics,ZhejiangUniversity,Hangzhou310027)Abstract:Analyticf... 相似文献