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Vector measures and the strong operator topology
Author(s):
Paul
Lewis;
Kimberly
Muller;
Andy
Yingst
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2345-2350.
MSC (2000):
Primary 28B05, 46B28, 46B25
Posted:
January 30, 2009
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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.
References:
-
- 1.
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- 2.
- R. Bilyeu and P. Lewis, Uniform differentiability, uniform absolute continuity, and the Vitali-Hahn-Saks theorem, Rocky Mtn. J. Math. 10(1980), 533-557. MR 590217 (82g:46083)
- 3.
- J. Diestel, Sequences and Series in Banach Spaces, Grad. Texts in Math. 92, Springer, New York, 1984. MR 737004 (85i:46020)
- 4.
- J. Diestel and J.J. Uhl, Jr., Vector Measures, Amer. Math. Soc., Providence, RI, 1977. MR 0453964 (56:12216)
- 5.
- N. Dunford and J. Schwartz, Linear Operators, Part I: General Theory, Wiley, New York, 1958. MR 1009162 (90g:47001a)
- 6.
- N. Kalton, Spaces of compact operators, Math. Ann. 208(1974), 267-278. MR 0341154 (49:5904)
- 7.
- H. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37(1970), 13-36. MR 0270122 (42:5015)
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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:
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
Posted:
January 30, 2009
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2009,
American Mathematical Society
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