RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (167 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517

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
\Bibitem{Ryb96} \by V.~I.~Rybakov \paper On convergence on the boundary of the unit ball in dual space \jour Mat. Zametki \yr 1996 \vol 59 \issue 5 \pages 753--758 \mathnet{http://mi.mathnet.ru/mz1769} \crossref{https://doi.org/10.4213/mzm1769} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1445456} \zmath{https://zbmath.org/?q=an:0888.46008} \transl \jour Math. Notes \yr 1996 \vol 59 \issue 5 \pages 543--546 \crossref{https://doi.org/10.1007/BF02308822} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1996VM73200011}