Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591821 | Journal of Functional Analysis | 2011 | 13 Pages |
Abstract
Let X be a rearrangement invariant function space on [0,1]. We consider the subspace Radi X of X which consists of all functions of the form , where xk are arbitrary independent functions from X and rk are usual Rademacher functions independent of {xk}. We prove that Radi X is complemented in X if and only if both X and its Köthe dual space X′ possess the so-called Kruglov property. As a consequence we show that the last conditions guarantee that X is isomorphic to some rearrangement invariant function space on [0,∞). This strengthens earlier results derived in different approach in [W.B. Johnson, B. Maurey, G. Schechtman, L. Tzafriri, Symmetric structures in Banach spaces, Mem. Amer. Math. Soc. 1 (217) (1979)].
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