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Subspaces Generated by Translations in Rearrangement Invariant Spaces

โœ Scribed by Francisco L. Hernandez; Evgueni M. Semenov

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
270 KB
Volume
169
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

In the setting of rearrangement invariant (r.i.) Banach function spaces E on [0, ) we study the complementability of subspaces Q a generated by sequences of translations of functions a # E[0, 1). An r.i. function space E is said to be nice (in short, E # N) if every subspace of type Q a is complemented. We give necessary and sufficient conditions for an r.i. function space to be nice. We determinate the Orlicz, Lorentz and Marcinkiewicz spaces belonging to the class N. As an application we obtain a new characterization of the L p -spaces, 1< p< , among the class of r.i. function spaces. 1999 Academic Press k=1 ( 0 xb k d+) a k is a norm-one projection from L p (+) onto [a k ].

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