GENERALIZED MEASURES OF NON-PRECOMPACTNESS RELATIVE TO VON-NEUMANN-ALGEBRAS

Suppose M is a von Neumann algebra on a Hilbert space re and I is any norm closed ideal in M. We will characterise I in terms of a generalis ed measure of non-precompactness on H which, in the case where;ll is t he algebra of all bounded operators on H and I is the ideal of compact operators, reduces to the classical ball measure of non-compactness. Now suppose M is a semifinite von Neumann algebra, tau a faithful semi finite normal trace on M, and kt the space of tau-measurable operators . We find generalised measures of non-precompactness on H which are pa rametrised by the positive half-line and which can be used to characte rise the ideal of tau-compact operators. (C) 1995 Academic Press, Inc.