FINITE REPRESENTABILITY OF lp-SPACES IN SYMMETRIC SPACES

For a separable rearrangement invariant space X on the semiaxis, F(X) is defined to be the set of all p is an element of [1, infinity] such that l(p) is finitely representable in X in such a way that the standard basis vectors of l(p) correspond to equimeasurable mutually disjoint functions. In the paper, a characterization of the set F(X) is obtained. As a consequence, a version of Krivine's well-known theorem is proved for rearrangement invariant spaces. Next, a description of the sets T(X) for certain Lorentz spaces is found.