Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Weakly compact subsets of symmetric operator spaces

Peter G. Doddsa1, Theresa K. Doddsa1 and Ben De Pagtera2

a1 School of Information Science & Technology, The Flinders University of South Australia, GPO Box 2100, Adelaide 5001, Australia

a2 Department of Mathematics, Delft University of Technology, Julianalaan 132, NL-2628 BL Delft, The Netherlands

Abstract

Under natural conditions it is shown that the rearrangement invariant hull of a weakly compact subset of a properly symmetric Banach space of measurable operators affiliated with a semi-finite von Neumann algebra is again relatively weakly compact.

(Received September 05 1990)