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The uniform Kadec-Klee property for the Lorentz spaces Lw,1
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1996
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