Non-commutative locally convex measures

J D Maitland Wright, Jose Bonet

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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, Saîto and Wright are extended to this more general setting. Building on an approach due to Saîto 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.
Original languageEnglish
Pages (from-to)21-38
Number of pages18
JournalQuarterly Journal of Mathematics
Volume62
Issue number1
Early online date2 Jun 2009
DOIs
Publication statusPublished - Mar 2011

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Weakly Compact Operators
Locally Convex Space
Finitely Additive Measure
Vector Measures
C*-algebra
Banach space
Topology
Theorem

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Non-commutative locally convex measures. / Wright, J D Maitland; Bonet, Jose.

In: Quarterly Journal of Mathematics, Vol. 62, No. 1, 03.2011, p. 21-38.

Research output: Contribution to journalArticle

Wright, J D Maitland ; Bonet, Jose. / Non-commutative locally convex measures. In: Quarterly Journal of Mathematics. 2011 ; Vol. 62, No. 1. pp. 21-38.
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