THE UNIFORM KADEC-KLEE PROPERTY FOR THE LORENTZ SPACES L(W,1)

Authors
DILWORTH SJ HSU YP
Citation
Sj. Dilworth et Yp. Hsu, THE UNIFORM KADEC-KLEE PROPERTY FOR THE LORENTZ SPACES L(W,1), Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 60, 1996, pp. 7-17
Citations number
16
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
60
Year of publication
1996
Part
1
Pages
7 - 17
Database
ISI
SICI code
0263-6115(1996)60:<7:TUKPFT>2.0.ZU;2-D
Abstract
In this paper we show that the Lorentz space L(w,1)(0,infinity) has th e weak-star uniform Kadec-Klee property if and only if inf(t>0)(w(alph a t)/w(t)) > 1 and sup(t>0)(phi(alpha t)/phi(t)) < 1 for all alpha eps ilon (0,1), where phi(t) = integral(0)(t) w(s) ds.