Embeddings of rearrangement invariant spaces that are not strictly singular

Authors
Montgomery-Smith, SJ Semenov, EM
Citation
Sj. Montgomery-smith et Em. Semenov, Embeddings of rearrangement invariant spaces that are not strictly singular, POSITIVITY, 4(4), 2000, pp. 397-402
Citations number
9
Categorie Soggetti
Mathematics
Journal title
POSITIVITY
ISSN journal
13851292 → ACNP
Volume
4
Issue
4
Year of publication
2000
Pages
397 - 402
Database
ISI
SICI code
1385-1292(2000)4:4<397:EORIST>2.0.ZU;2-A
Abstract
We give partial answers to the following conjecture: the natural embedding of a rearrangement invariant space E into L-1([0,1]) is strictly singular i f and only if G does not embed into E continuously, where G is the closure of the simple functions in the Orlicz space L-Phi with Phi>(*) over bar * ( x) = exp(x(2))-1.