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The uniform Kadec-Klee property for the Lorentz spaces Lw,1

Part of: Spaces with richer structures Linear function spaces and their duals Normed linear spaces and Banach spaces; Banach lattices General convexity Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

S. J. Dilworth  and
Yu-Ping Hsu
S. J. Dilworth
Affiliation:
Department of MathematicsUniversity of South CarolinaColumbia, SC 29208, USA
Yu-Ping Hsu
Affiliation:
Department of General StudiesNational Taiwan Ocean UniversityKeelung, TaiwanROC
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Abstract

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In this paper we show that the Lorentz space Lw, 1(0, ∞) has the weak-star uniform Kadec-Klee property if and only if inft>0 (w(αt)/w(t)) > 1 and supt>0(φ(αt) / φ(t))< 1 for all α ∈ (0, 1), where φ(t) = ∫t0 w(s) ds.

Keywords

Lorentz spaceuniform Kadec-Klee Propertyfixed point property.

MSC classification

Secondary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46B25: Classical Banach spaces in the general theory 54E40: Special maps on metric spaces 52A07: Convex sets in topological vector spaces 46A50: Compactness in topological linear spaces; angelic spaces, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 1 , February 1996 , pp. 7 - 17
Copyright
Copyright © Australian Mathematical Society 1996

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