Non-Commutative Locally Convex Measures

We study weakly compact operators from a C*-algebra with values in a complete locally convex space. They constitute a natural non-commutative generalization of finitely additive vector measures with values in a locally convex space. Several results of Brooks, Sato and Wright are extended to this more general setting. Building on an approach due to Sato and Wright, we obtain our theorems on non-commutative finitely additive measures with values in a locally convex space, from more general results on weakly compact operators defined on Banach spaces X whose strong dual X' is weakly sequentially complete. Weakly compact operators are also characterized by a continuity property for a certain 'Right topology' as in joint work by Peralta, Villanueva, Wright and Ylinen. © 2009. Published by Oxford University Press. All rights reserved.

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Quarterly Journal of Mathematics following peer review. The version of record: José Bonet and J. D. Maitland Wright Non-Commutative Locally Convex Measures Q J Math (2011) 62 (1): 21-38 first published online June 2, 2009 doi:10.1093/qmath/hap018 is available online at: http://qjmath.oxfordjournals.org/content/62/1/21