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Mat. Zametki, 1996, Volume 59, Issue 5, Pages 753–758 (Mi mz1769)  

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 $X$.

DOI: https://doi.org/10.4213/mzm1769

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

Bibliographic databases:

UDC: 517
Received: 10.05.1994

Citation: V. I. Rybakov, “On convergence on the boundary of the unit ball in dual space”, Mat. Zametki, 59:5 (1996), 753–758; Math. Notes, 59:5 (1996), 543–546

Citation in format AMSBIB
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\paper On convergence on the boundary of the unit ball in dual space
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\vol 59
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\pages 753--758
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\transl
\jour Math. Notes
\yr 1996
\vol 59
\issue 5
\pages 543--546
\crossref{https://doi.org/10.1007/BF02308822}
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