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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Vector measures and the strong operator topology


Authors: Paul Lewis, Kimberly Muller and Andy Yingst
Journal: Proc. Amer. Math. Soc. 137 (2009), 2345-2350
MSC (2000): Primary 28B05, 46B28, 46B25
Published electronically: January 30, 2009
Erratum: Proc. Amer. Math. Soc. 138 (2010), 3391
MathSciNet review: 2495268
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Abstract: A fundamental result of Nigel Kalton is used to establish a result for operator valued measures which has improved versions of the Vitali-Hahn-Saks Theorem, Phillips's Lemma, the Orlicz-Pettis Theorem and other classical results as straightforward corollaries.


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Additional Information

Paul Lewis
Affiliation: Department of Mathematics, University of North Texas, Box 311430, Denton, Texas 76203-1430

Kimberly Muller
Affiliation: Department of Mathematics and Computer Science, Lake Superior State University, 650 W. Easterday Avenue, Sault St. Marie, Michigan 49783-1699

Andy Yingst
Affiliation: Department of Mathematics, University of South Carolina, P.O. Box 889, Lancaster, South Carolina 29721

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09797-4
PII: S 0002-9939(09)09797-4
Keywords: Operator valued measure, strong operator topology, Phillips's lemma, Orlicz-Pettis theorem
Received by editor(s): December 20, 2007
Received by editor(s) in revised form: September 16, 2008
Published electronically: January 30, 2009
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2009 American Mathematical Society