BOUNDEDLY COMPLETE BASIC SEQUENCES, C(0)-SUBSPACES, AND INJECTIONS OF BANACH-SPACES

被引：7
作者：
FONF, VP
机构：
[1] Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, 84105
来源：
ISRAEL JOURNAL OF MATHEMATICS | 1995年 / 89卷 / 1-3期
关键词：
D O I：
10.1007/BF02808199
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the connection between topological properties of subsets of a given Banach space and their images under linear, continuous one-to-one mappings on the one hand and the existence in a given Banach space of either a boundedly complete basic sequence (BCBS) or an isomorphic copy of c(o) (c(o)-subspace) on the other band. We present criteria for the existence of a BCBS. They are deduced from new characterisations of G(delta)-embeddings which we also present. We obtain a necessary and sufficient condition for separability of a dual Banach space in terms of saturation by BCBS. Criteria for the existence in a Banach space of a c(o)-subspace are also presented. We describe the class of separable Banach spaces which contains either a BCBS or a c(o)-subspace.
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收藏
页码：173 / 188
页数：16
相关论文
共 17 条
[1]  
Bourgain J., Rosenthal H.P., Applications of the theory of semi-embeddings to Banach space theory, Journal of Functional Analysis, 52, pp. 149-188, (1983)
[2]  
Edgar G.A., Wheeler R.F., Topological properties of Banach spaces, Pacific Journal of Mathematics, 115, pp. 317-350, (1984)
[3]  
Fonf V.P., On polyhedral Banach spaces, Matematicheskie Zametki, 30, pp. 627-634, (1981)
[4]  
Fonf V.P., On injections of Banach spaces with closed image of the unit ball, Funktsionalnyi Analiz i ego Prilozheniya, 19, pp. 87-88, (1985)
[5]  
Fonf V.P., On semi-embeddings and G<sub>δ</sub>- embeddings of Banach spaces, Matematicheskie Zametki, 39, pp. 550-561, (1986)
[6]  
Fonf V.P., Dual subspaces and injections of Banach spaces, Ukrainski Matematicheski Zhurnal, 39, pp. 364-369, (1987)
[7]  
Fonf V.P., On Borelian type of the set of convergence of the sequence linear bounded operators in Banach space, Teoriya Funktsii, Funktsional’nyi Analiz ikh Prilozheniya, 50, pp. 90-98, (1988)
[8]  
Fonf V.P., Sets of the super-first category in Banach spaces, Funktsionalnyi Analiz i ego Prilozeniya, 25, pp. 66-69, (1991)
[9]  
Ghoussoub N., Maurey B., G<sub>δ</sub>- embeddings in Hilbert space, Journal of Functional Analysis, 61, pp. 72-97, (1985)
[10]  
Ghoussoub N., Maurey B., G<sub>δ</sub>- embeddings in Hilbert space (part 2), Journal of Functional Analysis, 78, pp. 271-305, (1988)
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