CHARACTERIZATIONS OF KADEC-KLEE PROPERTIES IN SYMMETRICAL SPACES OF MEASURABLE FUNCTIONS

Authors
CHILIN VI DODDS PG SEDAEV AA SUKOCHEV FA
Citation
Vi. Chilin et al., CHARACTERIZATIONS OF KADEC-KLEE PROPERTIES IN SYMMETRICAL SPACES OF MEASURABLE FUNCTIONS, Transactions of the American Mathematical Society, 348(12), 1996, pp. 4895-4918
Citations number
24
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
348
Issue
12
Year of publication
1996
Pages
4895 - 4918
Database
ISI
SICI code
0002-9947(1996)348:12<4895:COKPIS>2.0.ZU;2-1
Abstract
We present several characterizations of Kadec-Klee properties in symme tric function spaces on the half-line, based on the K-functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respecti vely local convergence in measure) on the unit sphere coincides with n orm convergence.