共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
R.A. McCoy 《Topology and its Applications》2010,157(16):2516-2537
A study is made of two classes of product topologies on powers of spaces: the general box product topologies, and the general uniform product topologies. Some examples are given and some results are shown about the properties of these general product spaces. This is applied to show that certain spaces of continuous functions with the fine topology are homeomorphic to box product spaces, and certain spaces of continuous functions with the uniform topology are homeomorphic to uniform product spaces. 相似文献
3.
Daniel Carando Verónica Dimant Santiago Muro 《Journal of Mathematical Analysis and Applications》2007,336(2):1324-1340
A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on Cn, which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces of holomorphic functions on a Banach space. In this work, we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators. Some known results come out as particular cases of this setting. We also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the Schatten-von Neumann class. 相似文献
4.
Piotr Koszmider 《Proceedings of the American Mathematical Society》2005,133(7):2137-2146
It is well known that if is infinite compact Hausdorff and scattered (i.e., with no perfect subsets), then the Banach space of continuous functions on has complemented copies of , i.e., . We address the question if this could be the only type of decompositions of into infinite-dimensional summands for infinite, scattered. Making a special set-theoretic assumption such as the continuum hypothesis or Martin's axiom we construct an example of Mrówka's space (i.e., obtained from an almost disjoint family of sets of positive integers) which answers positively the above question.
5.
6.
Geraldo Botelho Daniel Pellegrino 《Journal of Mathematical Analysis and Applications》2006,321(1):50-58
If X is a Banach space with a normalized unconditional Schauder basis (xn), we define whenever and obtain estimates for μX,(xn) when every continuous m-homogeneous polynomial from X into Y is absolutely (q,1) summing. Our results provide new information on coincidence situations between the space of absolutely summing m-homogeneous polynomials and the whole space of continuous m-homogeneous polynomials. In particular, when m=1, we obtain new contributions to the linear theory of absolutely summing operators. 相似文献
7.
M. I. Gil' 《Mathematische Nachrichten》2008,281(8):1129-1141
Analytic operator valued functions of two operators on tensor products of Hilbert spaces are considered. A precise norm estimate is established. Applications to operator differential equations are also discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
Fernando Bombal Ignacio Villanueva 《Proceedings of the American Mathematical Society》2001,129(5):1359-1363
In this paper we characterize those compact Hausdorff spaces such that (and ) have the Dunford-Pettis Property, answering thus in the negative a question posed by Castillo and González who asked if and have this property.
9.
David Pérez-García Ignacio Villanueva 《Journal of Mathematical Analysis and Applications》2005,306(1):97-105
We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y, there exists a linear operator S:C(K)→Y such that P(f)=S(fn). This is the C(K) version of a related result of Sundaresam for polynomials on Lp spaces. 相似文献
10.
Ignacio Villanueva 《Czechoslovak Mathematical Journal》2004,54(2):373-378
We use polymeasures to characterize when a multilinear form defined on a product of C(K, X) spaces is integral. 相似文献
11.
We study integral refinable operators of integral type exact on polynomials of even degree constructed by using refinable B-bases of GP type. We prove a general theorem of existence and uniqueness. Then we study the Lp-norm of these operators and we give error bounds in approximating functions and their derivatives belonging to suitable classes. Numerical results and comparisons with other quasi-interpolatory operators having the same order of exactness on polynomial reproduction are presented. 相似文献
12.
Damián Pinasco 《Journal of Mathematical Analysis and Applications》2005,308(1):159-174
In this paper we discuss the problem of integral representation of analytic functions over a complex Banach space E. We obtain, for a wide class of functions, integral representations of the form
13.
A subset A of a metric space X is said to be a nonexpansive proximinal retract (NPR) of X if the metric projection from X to A admits a nonexpansive selection. We study the structure of NPR's in the space C(K) of continuous functions on a compact Hausdorff space K. The main results are a characterization of finite-codimensional and of finite-dimensional NPR subspaces of C(K) and a complete characterization of all NPR subsets of . 相似文献
14.
J.S. Manhas 《Applied mathematics and computation》2011,218(3):929-934
Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let UX and UY be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on UX and UY, respectively. Let HV(UX, E) (or HV0(UX, E)) and HW(UY, F) (or HW0(UY, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings ? : UY → UX and ψ : UY → B(E, F) which generate weighted composition operators between these weighted spaces. 相似文献
15.
We show that every Banach space X whose centralizer is infinite-dimensional satisfies that every non-empty weakly open set in BY has diameter 2, where (N-fold symmetric projective tensor product of X, endowed with the symmetric projective norm), for every natural number N. We provide examples where the above conclusion holds that includes some spaces of operators and infinite-dimensional C∗-algebras. We also prove that every non-empty weak∗ open set in the unit ball of the space of N-homogeneous and integral polynomials on X has diameter two, for every natural number N, whenever the Cunningham algebra of X is infinite-dimensional. Here we consider the space of N-homogeneous integral polynomials as the dual of the space (N-fold symmetric injective tensor product of X, endowed with the symmetric injective norm). For instance, every infinite-dimensional L1(μ) satisfies that its Cunningham algebra is infinite-dimensional. We obtain the same result for every non-reflexive L-embedded space, and so for every predual of an infinite-dimensional von Neumann algebra. 相似文献
16.
Klaus Floret Stephan Hunfeld 《Proceedings of the American Mathematical Society》2002,130(5):1425-1435
Using the theory of full and symmetric tensor norms on normed spaces, a theorem of Kürsten and Heinrich on ultrastability and maximality of normed operator ideals is extended to ideals of -homogeneous polynomials and -linear mappings--scalar-valued and vector-valued. The motivation for these results is the following important special case: the ``uniterated' Aron-Berner extension : of an -homogeneous polynomial to the bidual remains in certain ideals under preservation of the norm. Moreover, Lotz's characterization of maximal normed ideals of linear mappings through appropriate tensor norms is proved for ideals of -homogeneous scalar-valued polynomials and ideals of -linear mappings.
17.
Antonio Bonilla Pedro J. Miana 《Proceedings of the American Mathematical Society》2008,136(2):519-528
Our first aim in this paper is to give sufficient conditions for the hypercyclicity and topological mixing of a strongly continuous cosine function. We apply these results to study the cosine function associated to translation groups. We also prove that every separable infinite dimensional complex Banach space admits a topologically mixing uniformly continuous cosine family.
18.
Bogdan C. Grecu Raymond A. Ryan 《Proceedings of the American Mathematical Society》2005,133(4):1083-1091
We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.
19.
Alex Chigogidze 《Proceedings of the American Mathematical Society》2001,129(10):2959-2963
We show that complemented subspaces of uncountable products of Banach spaces are products of complemented subspaces of countable subproducts.
20.
Eve Oja 《Proceedings of the American Mathematical Society》2007,135(11):3581-3587
Inspired by the principle of local reflexivity, due to Lindenstrauss and Rosenthal, a new geometric property of Banach spaces, the extendable local reflexivity, was recently introduced by Rosenthal. Johnson and Oikhberg proved that the extendable local reflexivity permits lifting the bounded approximation property from Banach spaces to their dual spaces. It is not known whether the extendable local reflexivity permits lifting the approximation property. We prove that it does whenever the space is complemented in its bidual. This involves the concept of the weak bounded approximation property, introduced by Lima and Oja.