Abstract. In this note we show that the number of isomorphism classes of complemented subspaces of a reflexive Orlicz function space LΦ[0,1] is un- countable, as soon as LΦ[0,1] is not isomorphic to L2[0,1]. Also, we prove that the set of all separable Banach spaces that are isomorphic to such an LΦ[0,1] is analytic non-Borel. Moreover, by using the Boyd interpolation the- orem we extend some results on Lp [0, 1] spaces to the rearrangement invariant function spaces under natural conditions on their Boyd indices. 

Title

Proceeding of the American Mathematical Society

Publisher

American Mathematical Society

Publisher Country

United States of America

Indexing

Thomson Reuters

Impact Factor

0.681

Publication Type

Both (Printed and Online)

Volume

144

Year

2016

Pages

285-299