Abstract
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.
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M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. I,Functional Analysis [Russian translation] Mir, Moscow (1977).
H. Schaefer,Topological Vector Spaces [Russian translation], Mir, Moscow (1971).
S. L. Sobolev,Selected Problems of the Theory of Functional Spaces and Generalized Functions [in Russian], Nauka, Moscow (1989).
W. Rudin,Functional Analysis [Russian translation], Mir, Moscow (1975).
A. Yosida,Functional Analysis, [Russian translation], Mir, Moscow (1967).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp 731–739, June. 2000.
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Kogut, P.I., Mel'nik, V.S. On weak compactness of bounded sets in Banach and locally convex spaces. Ukr Math J 52, 837–846 (2000). https://doi.org/10.1007/BF02591778
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DOI: https://doi.org/10.1007/BF02591778