共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove the existence of a simultaneous projectional skeleton for certain subspaces of C(K) spaces. This generalizes a result on simultaneous projectional resolutions of identity proved by M. Valdivia. We collect some consequences of this result. In particular we give a new characterization of Asplund spaces using the notion of projectional skeleton. 相似文献
2.
María D. Acosta Angel Rodríguez-Palacios 《Journal of Mathematical Analysis and Applications》2011,383(2):461-473
A Banach space is said to have the diameter two property if every non-empty relatively weakly open subset of its unit ball has diameter two. We prove that the projective tensor product of two Banach spaces whose centralizer is infinite-dimensional has the diameter two property. The same statement also holds for if the centralizer of X is infinite-dimensional and the unit sphere of Y? contains an element of numerical index one. We provide examples of classical Banach spaces satisfying the assumptions of the results. If K is any infinite compact Hausdorff topological space, then has the diameter two property for any nonzero Banach space Y. We also provide a result on the diameter two property for the injective tensor product. 相似文献
3.
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a Banach space. This completely generalizes a well-known result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group. We also prove that isometric group representation induced framings on a Banach space can be dilated to unconditional bases with the same structure for a larger Banach space. This extends several known results on the dilations of frames induced by unitary group representations on Hilbert spaces. 相似文献
4.
Wies?aw Kubi? 《Topology and its Applications》2007,154(3):749-757
We construct a compact linearly ordered space Kω1 of weight ℵ1, such that the space C(Kω1) is not isomorphic to a Banach space with a projectional resolution of the identity, while on the other hand, Kω1 is a continuous image of a Valdivia compact and every separable subspace of C(Kω1) is contained in a 1-complemented separable subspace. This answers two questions due to O. Kalenda and V. Montesinos. 相似文献
5.
It is proved that every non-trivial weak-Cauchy sequence in a Banach space with the PCP (the Point of Continuity Property) has a boundedly complete basic subsequence. The following result, due independently to S. Bellenot and C. Finet, is then deduced as a corollary. If a Banach space X has separable dual and the PCP, then every non-trivial weak-Cauchy sequence in X has a subsequence spanning an order-one quasi-reflexive space. 相似文献
6.
We investigate the diagonal sequence property in Banach spaces with weaker topologies. In particular, we present examples of Banach spaces with weaker locally convex topologies which have the diagonal sequence property but are not Fréchet–Urysohn. The examples answer negatively a question of Averbukh and Smolyanov. We give also a very simple proof of the fact that each Banach space contains a subset A whose weak closure includes 0, but 0 is not contained in the weak closure of any bounded subset of A. 相似文献
7.
We show that every pseudoconvex open subset of a Banach space with an unconditional Schauder basis has the F-valued Runge property for every Banach space F. 相似文献
8.
Stuart F. Cullender 《Journal of Mathematical Analysis and Applications》2007,326(2):1291-1309
For a Banach space Y, the question of whether Lp(μ,Y) has an unconditional basis if 1<p<∞ and Y has unconditional basis, stood unsolved for a long time and was answered in the negative by Aldous. In this work we prove a weaker, positive result related to this question. We show that if (yj) is a basis of Y and (di) is a martingale difference sequence spanning Lp(μ) then the sequence (di⊗yj) is a basis of Lp(μ,Y) for 1?p<∞. Moreover, if 1<p<∞ and (yj) is unconditional then (di⊗yj) is strictly dominated by an unconditional tensor product basis. In addition, for 1<p<∞, we show that if (di)⊂Lp(μ) is a martingale difference sequence then there exists a constant K>0 so that
9.
We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable if and only if it is Corson. This gives an answer to a question of R. Rojas-Hernández and V.V. Tkachuk. Further, we apply this result to characterize retractional skeleton using a topology on the space of continuous functions, answering thus a question of the first author and a related question of W. Kubi?. 相似文献
10.
José Rodríguez 《Journal of Mathematical Analysis and Applications》2008,341(1):80-90
We show that McShane and Pettis integrability coincide for functions , where μ is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelöf determined Banach space X, a scalarly null (hence Pettis integrable) function and an absolutely summing operator u from X to another Banach space Y such that the composition is not Bochner integrable; in particular, h is not McShane integrable. 相似文献
11.
Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, and a nonexpansive self-mappings semigroup of K, and a fixed contractive mapping. The strongly convergent theorems of the following implicit and explicit viscosity iterative schemes {xn} are proved.
xn=αnf(xn)+(1−αn)T(tn)xn, 相似文献
12.
Olga Polverino 《Discrete Mathematics》2010,310(22):3096-3107
In this paper linear sets of finite projective spaces are studied and the “dual” of a linear set is introduced. Also, some applications of the theory of linear sets are investigated: blocking sets in Desarguesian planes, maximum scattered linear sets, translation ovoids of the Cayley Hexagon, translation ovoids of orthogonal polar spaces and finite semifields. Besides “old” results, new ones are proven and some open questions are discussed. 相似文献
13.
This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent. 相似文献
14.
Jos Rodríguez 《Journal of Mathematical Analysis and Applications》2009,350(2):80-524
We show that McShane and Pettis integrability coincide for functions , where μ is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelöf determined Banach space X, a scalarly null (hence Pettis integrable) function and an absolutely summing operator u from X to another Banach space Y such that the composition is not Bochner integrable; in particular, h is not McShane integrable. 相似文献
15.
Michael Doré 《Journal of Functional Analysis》2011,261(6):1674-1710
We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Fréchet differentiable somewhere in S. 相似文献
16.
We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges. 相似文献
17.
Suyalatu 《Journal of Mathematical Analysis and Applications》2004,298(1):45-56
In this paper, we introduce two types of new Banach spaces: k-super-strongly convex spaces and k-super-strongly smooth spaces. It is proved that these two notions are dual. We also prove that the class of k-super-strongly convexifiable spaces is strictly between locally k-uniformly rotund spaces and k-strongly convex spaces, and obtain some necessary and sufficient conditions of k-super-strongly convex space (respectively k-super-strongly smooth space). Also, for each k?2, it is shown that there exists a k-super-strongly convex (respectively k-super-strongly smooth) space which is not (k−1)-super-strongly convex (respectively (k−1)-super-strongly smooth) space. 相似文献
18.
Eberhard Kaniuth 《Journal of Functional Analysis》2008,254(4):987-1002
Let A be a semisimple and regular commutative Banach algebra with structure space Δ(A). Generalizing the notion of spectral sets in Δ(A), the considerably larger class of weak spectral sets was introduced and studied in [C.R. Warner, Weak spectral synthesis, Proc. Amer. Math. Soc. 99 (1987) 244-248]. We prove injection theorems for weak spectral sets and weak Ditkin sets and a Ditkin-Shilov type theorem, which applies to projective tensor products. In addition, we show that weak spectral synthesis holds for the Fourier algebra A(G) of a locally compact group G if and only if G is discrete. 相似文献
19.
Let X and Y be two Banach spaces. In this short note we show that every weakly compact subset in the projective tensor product of X and Y can be written as the intersection of finite unions of sets of the form , where KX and KY are weakly compacts subsets of X and Y, respectively. If either X or Y has the Dunford–Pettis property, then any intersection of sets that are finite unions of sets of the form , where KX and KY are weakly compact sets in X and Y, respectively, is weakly compact. 相似文献
20.
A. V. Romanov 《Mathematical Notes》2007,82(5-6):806-815
We propose a natural analog of the Wold decomposition in the case of a linear noninvertible isometry V in a Banach space X. We obtain a criterion for the existence of such a decomposition. In a reflective space, this criterion is reduced to the existence of the linear projection P: X → VX with unit norm. Separately, we discuss the problem of the Wold decomposition for the isometry V φ induced by an epimorphism φ of a compact set H in the space of continuous functions C(H). We present a detailed study of the mapping z → z m of the circle |z| = 1 with an integer m ≥ 2. 相似文献