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AN ELEMENTARY PROOF OF JAMES’ CHARACTERIZATION OF WEAK COMPACTNESS

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  03 June 2011

WARREN B. MOORS
WARREN B. MOORS*
Affiliation:
Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand (email: moors@math.auckland.ac.nz)
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Abstract

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In this paper we provide an elementary proof of James’ characterization of weak compactness in separable Banach spaces. The proof of the theorem does not rely upon either Simons’ inequality or any integral representation theorems. In fact the proof only requires the Krein–Milman theorem, Milman’s theorem and the Bishop–Phelps theorem.

Keywords

compact convex setsboundariesRainwater’s theoremKrein–Milman theorem

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 98 - 102
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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