共查询到20条相似文献,搜索用时 15 毫秒
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Giovanni Emmanuele 《Annali di Matematica Pura ed Applicata》1988,152(1):171-181
Summary We consider the Banach spaces with the property (V*) of Pelczynski giving a sufficient condition for a Banach space to have this property as well as a characterization of Banach lattices with the same property. Several other results are given which are concerning relationships among that property and other famous isomorphic properties of Banach spaces. Also a characterization of Banach spaces with property (V*) using Schauder decompositions is given. Some result concerning lifting of that property from a Banach space E to L1(, E) is presented, too.Work performed under the auspices of G.N.A.F.A. of C.N.R. and partially supported by M.P.I. of Italy (40%). 相似文献
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Erhan Çalişkan 《Czechoslovak Mathematical Journal》2007,57(2):763-776
We show that a Banach space E has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on E can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials
generated by weakly compact linear operators. An analogous result is established also for the compact approximation property. 相似文献
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Fully symmetric operator spaces 总被引:4,自引:0,他引:4
Peter G. Dodds Theresa K. Dodds Ben de Pagter 《Integral Equations and Operator Theory》1992,15(6):942-972
It is shown that certain interpolation theorems for non-commutative symmetric operator spaces can be deduced from their commutative versions. A principal tool is a refinement of the notion of Schmidt decomposition of a measurable operator affiliated with a given semi-finite von Neumann algebra.Research supported by A.R.C. 相似文献
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《Journal of Functional Analysis》2023,284(10):109889
We introduce a measure of super weak noncompactness Γ defined for bounded subsets and bounded linear operators in Banach spaces that allows to state and prove a characterization of the Banach spaces which are subspaces of a Hilbert-generated space. The use of super weak compactness and Γ casts light on the structure of these Banach spaces and complements the work of Argyros, Fabian, Farmaki, Godefroy, Hájek, Montesinos, Troyanski and Zizler on this subject. A particular kind of relatively super weakly compact sets, namely uniformly weakly null sets, plays an important role and exhibits connections with Banach-Saks type properties. 相似文献
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Giovanni Emmanuele 《Annali di Matematica Pura ed Applicata》1991,160(1):163-170
Summary We present a converse of a result contained in our paper «On the Banach spaces with the property (V*) of Pelczynski» so obtaining a characterization of that family of Banach spaces. Hence some extensions of other results from that note are presented. At the end we study property (V*) in spaces of operators with compact range.The results of this paper were obtained during the permanence of the author at Kent State University, Kent, Ohio 44242, U.S.A. thanks to a fellowship of the Italian C.N.R. 相似文献
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Volker Runde 《Expositiones Mathematicae》2004,22(4):317-363
We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras). 相似文献
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We show that ifX is a Banach space of type 2 andG is a compact Abelian group, then any system of eigenvectors {x
}G
(with respect to a strongly continuous representation ofG onX) is an RUC-system. As an application, we exhibit new examples of RUC-bases in certain symmetric spaces of measurable operators.Research supported by the Australian Research Council 相似文献
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We show that (generalized) Calkin correspondence between quasi-normed symmetric sequence spaces and symmetrically quasi-normed ideals of compact operators on an infinite-dimensional Hilbert space preserves completeness. We also establish a semifinite version of this result. 相似文献
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GAO Mingchu Department of Mathematics University of Illinois at Urbana-Champaign Urbana IL USA 《中国科学A辑(英文版)》2006,49(6):800-819
Certain free products are introduced for operator spaces and dual operator spaces. It is shown that the free product of operator spaces does not preserve the injectivity. The linking C*-algebra of the full free product of two ternary rings of operators (simply, TRO's) is *-isomorphic to the full free product of the linking C*-algebras of the two TRO's. The operator space-reduced free product of the preduals of von Neumann algebras agrees with the predual of the reduced free product of the von Neumann algebras. Each of two operator spaces can be embedded completely isometrically into the reduced free product of the operator spaces. Finally, an example is presented to show that the C*-algebra-reduced free product of two C*-algebras may be contractively isomorphic to a proper subspace of their reduced free product as operator spaces. 相似文献
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Ioana Ghenciu 《Proceedings of the American Mathematical Society》2005,133(9):2621-2623
Classical results of Kalton are used to study the complementation of the space of weakly compact operators and the space of compact operators in the space of bounded linear operators from to .
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Zhe Dong 《Journal of Mathematical Analysis and Applications》2007,336(2):1054-1060
In this paper, we define and study the approximately local lifting property for operator spaces. We show that an operator space V has the approximately local lifting property if and only if V∗ is injective. This implies that an operator space V has the approximately local lifting property if and only if it has the local lifting property. 相似文献
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We obtain the K-groups of the operator ideals contained in the class of Riesz operators. And based on the results, we calculate the K-groups of the operator algebras on HD nspaces and QDn spaces. 相似文献
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F. A. Sukochev 《Integral Equations and Operator Theory》1996,26(1):102-124
If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if ·
E(M,)
is not proportional to ·
L
2, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council 相似文献
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We introduce a new tensor product and study the weak∗ condition C′, which is also called weak∗ exactness, for dual operator spaces. Our definition of weak∗ condition C′ is equivalent to Kirchberg's notion of weak exactness in the case of von Neumann algebras. We also study the connection of weak∗ exact W∗-TROs with their linking von Neumann algebras and study the structure of exact (respectively, nuclear) W∗-TROs. 相似文献