Condition of conjugacy of WCG-spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1978 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 23, pages 152-153 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Plichko, A. N.;

doi: 10.1007/bf01153158

Condition of conjugacy of WCG-spaces

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Abstract

It is proved that a WCG-space E is conjugate to a Banach space if and only if its conjugate space E′ contains a norm-closed total subspace M, consisting of functionals which attain supremum on the unit sphere. Moreover, M′ = E in the duality established between E and E′. An example, showing that this statement is in general not true for an arbitrary Banach space, is given.

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Keywords

Duality and reflexivity in normed linear and Banach spaces, WCG-spaces, conjugacy

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