This article is cited in 2 papers

Condition of conjugacy of $WCG$-spaces

A. N. Plichko

Kiev State University

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 Eprime. An example, showing that this statement is in general not true for an arbitrary Banach space, is given.

UDC: 517

Received: 06.10.1976

 English version: Mathematical Notes, 1978, 23:2, 152–153

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