RADIAL LIMIT OF LACUNARY FOURIER SERIES WITH COEFFICIENTS IN NON-COMMUTATIVE SYMMETRIC SPACES

摘要

Let E be n rearrangement invariant space, ∧ (∪) Z an arbitrary set and (M, r) a von Neumann algebra with a semifinite normal faithful trace. It is proved that the associated symmetric space of measurable operators E(M, r) has A-RNP if and only if E has ∧-RNP extending in this way some previous results in [X1], [X2].