NON-ISOMORPHIC COMPLEMENTED SUBSPACES OF THE REFLEXIVE ORLICZ FUNCTION SPACES L-Phi[0,1]

摘要

In this note we show that the number of isomorphism classes of complemented subspaces of a reflexive Orlicz function space L-Phi[0, 1] is uncountable, as soon as L-Phi[0, 1] is not isomorphic to L-2[0, 1]. Also, we prove that the set of all separable Banach spaces that are isomorphic to such an L-Phi[0, 1] is analytic non-Borel. Moreover, by using the Boyd interpolation theorem we extend some results on L-p[0, 1] spaces to the rearrangement invariant function spaces under natural conditions on their Boyd indices.