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Uniform Kadec-Klee Lorentz Spaces Lw,1 and Uniformly Concave Functions
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 1996
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