THE KADEC-KLEE PROPERTY IN 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 if and only if , for every semifinite von Neumann algebra (M,tau), the associated spa ce E(M,tau) of tau-measurable operators has the Kadec-Klee property.