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Uniform Kadec-Klee Lorentz Spaces Lw,1 and Uniformly Concave Functions

Published online by Cambridge University Press:  20 November 2018

S. J. Dilworth  and
C. J. Lennard
S. J. Dilworth
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A., e-mail:dilworth@math.scarolina.edu
C. J. Lennard
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A., e-mail:chris@lennext.math.pitt.edu
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Abstract

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We consider the notion of a uniformly concave function, using it to characterize those Lorentz spaces Lw,1 that have the weak-star uniform Kadec-Klee property as precisely those for which the antiderivative ϕ of w is uniformly concave; building on recent work of Dilworth and Hsu. We also derive a quite general sufficient condition for a twice-differentiable ϕ to be uniformly concave; and explore the extent to which this condition is necessary.

Keywords

Primary: 46Esecondary: 46BLorentz spacesuniform Kadec-Klee propertyweak-star convergenceuniformly concave functions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 3 , 01 September 1996 , pp. 266 - 274
Copyright
Copyright © Canadian Mathematical Society 1996

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