This article is cited in 1 paper

Banach Spaces with the PC Property

V. I. Rybakov

Tula State Pedagogical University

Abstract: A Banach space $X$ possesses the PC (point of continuity) property if for any $w$-closed bounded subset $A\subset X$ the identity map $(A,w)\to(A,\|\cdot\|)$ has a point of continuity ($w$ is the weak topology in $X$). We deduce some criteria for Banach spaces to have the PC property and describe (for dual Banach spaces) relationships between spaces possessing the PC property and spaces possessing the RN or the WRN property.

UDC: 517.98

Received: 20.01.2003

DOI: 10.4213/mzm132

 English version: Mathematical Notes, 2004, 76:4, 525–533

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