On weak compactness of bounded sets in banach and locally convex spaces

被引：0

作者：

Kogut P.I. ^{[1
]}

Mel'nik V.S. ^{[2
]}

机构：

[1] Dnepropetrovsk University, Dnepropetrovsk

[2] Institute of Applied Systems of Analysis, Ukrainian Academy of Sciences, Ukrainian Ministry of Education, Kiev

来源：

Ukrainian Mathematical Journal | 2000年 / 52卷 / 6期

关键词：

Banach Space; Weak Topology; Adjoint Operator; Convex Space; Admissible Control;

D O I：

10.1007/BF02591778

中图分类号：

学科分类号：

摘要：

We investigate the compactness of one class of bounded subsets in Banach and locally convex spaces. We obtain a generalization of the Banach-Alaoglu theorem to a class of subsets that are not polars of convex balanced neighborhoods of zero. © 2000 Kluwer Academic/Plenum Publishers.

引用

页码：837 / 846

页数：9

共 5 条

[1] Reed, M., Simon, B., (1977) Methods of Modem Mathematical Physics, Vol.1, Functional Analysis, 1. , [Russian translation], Mir, Moscow
[2] Schaefer, H., (1971) Topological Vector Spaces, , [Russian translation], Mir, Moscow
[3] Sobolev, S.L., (1989) Selected Problems of the Theory of Functional Spaces and Generalized Functions [in Russian], , Nauka, Moscow
[4] Rudin, W., (1975) Functional Analysis, , [Russian translation], Mir, Moscow
[5] Yosida, A., (1967) Functional Analysis, , [Russian translation], Mir, Moscow

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