LIFTING OF KADEC-KLEE PROPERTIES TO SYMMETRICAL SPACES OF MEASURABLE OPERATORS

We Show that if E is a separable symmetric Banach function space on th e positive half-line, then E has the Kadec-Klee property (respectively , uniform Kadec-Klee property) for local convergence in measure if and only if, for every semifinite von Neumann algebra (M,tau), the associ ated space E(M,tau) of tau-measurable operators has the same property.