Vector measures and the strong operator topology
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- by Paul Lewis, Kimberly Muller and Andy Yingst PDF
- Proc. Amer. Math. Soc. 137 (2009), 2345-2350 Request permission
Erratum: Proc. Amer. Math. Soc. 138 (2010), 3391-3391.
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
- C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI 10.4064/sm-17-2-151-164
- Russell G. Bilyeu and Paul W. Lewis, Uniform differentiability, uniform absolute continuity and the Vitali-Hahn-Saks theorem, Rocky Mountain J. Math. 10 (1980), no. 3, 533–557. MR 590217, DOI 10.1216/RMJ-1980-10-3-533
- Joseph Diestel, Sequences and series in Banach spaces, Graduate Texts in Mathematics, vol. 92, Springer-Verlag, New York, 1984. MR 737004, DOI 10.1007/978-1-4612-5200-9
- J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
- N. J. Kalton, Spaces of compact operators, Math. Ann. 208 (1974), 267–278. MR 341154, DOI 10.1007/BF01432152
- Haskell P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13–36. MR 270122, DOI 10.4064/sm-37-1-13-36
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
- 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
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2345-2350
- MSC (2000): Primary 28B05, 46B28, 46B25
- DOI: https://doi.org/10.1090/S0002-9939-09-09797-4
- MathSciNet review: 2495268