This article is cited in 3 papers

On convergence on the boundary of the unit ball in dual space

V. I. Rybakov

Tula State Pedagogical University

Abstract: In this paper some results that are known for extreme points of the unit ball in dual space are carried over to a more general case, namely to the case of the boundary of the ball ($\Gamma\subset B$ is the boundary of the unit ball $B$ in the space dual to $X$ if every $x\in X$ achieves its maximum value on $B$ at some point of $\Gamma$). For example, it is established that if a set is bounded in $X$ and countably compact in $\sigma(X,\Gamma)$, then it is weakly compact in $X$.

UDC: 517

Received: 10.05.1994

DOI: 10.4213/mzm1769

 English version: Mathematical Notes, 1996, 59:5, 543–546

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