Geodesic
Uniform Kadec-Klee Lorentz Spaces L w,1 and Uniformly Concave Functions
Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 266-274

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DOI

We consider the notion of a uniformly concave function, using it to characterize those Lorentz spaces L w,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.
DOI : 10.4153/CMB-1996-034-1
Mots-clés : Primary: 46E, secondary: 46B, Lorentz spaces, uniform Kadec-Klee property, weak-star convergence, uniformly concave functions 
Dilworth, S. J.; Lennard, C. J. Uniform Kadec-Klee Lorentz Spaces L w,1 and Uniformly Concave Functions. Canadian mathematical bulletin, Tome 39 (1996) no. 3, pp. 266-274. doi: 10.4153/CMB-1996-034-1
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     title = {Uniform {Kadec-Klee} {Lorentz} {Spaces} {L} w,1 and {Uniformly} {Concave} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {266--274},
     year = {1996},
     volume = {39},
     number = {3},
     doi = {10.4153/CMB-1996-034-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-034-1/}
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