Sequences in the range of a vector measure with bounded variation
HTML articles powered by AMS MathViewer
- by Cándido Piñeiro
- Proc. Amer. Math. Soc. 123 (1995), 3329-3334
- DOI: https://doi.org/10.1090/S0002-9939-1995-1291790-5
- PDF | Request permission
Abstract:
Let X be a Banach space. We consider sequences $({x_n})$ in X lying in the range of a measure valued in a superspace of X and having bounded variation. Among other results, we prove that G.T. spaces are the only Banach spaces in which those sequences are actually in the range of an ${X^{ \ast \ast }}$-valued measure of bounded variation.References
- R. Anantharaman and J. Diestel, Sequences in the range of a vector measure, Comment. Math. Prace Mat. 30 (1991), no. 2, 221–235. MR 1122692
- 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, DOI 10.1090/surv/015
- Albrecht Pietsch, Quasinukleare Abbildungen in normierten Räumen, Math. Ann. 165 (1966), 76–90 (German). MR 198253, DOI 10.1007/BF01351669
- Albrecht Pietsch, Operator ideals, North-Holland Mathematical Library, vol. 20, North-Holland Publishing Co., Amsterdam-New York, 1980. Translated from German by the author. MR 582655
- Cándido Piñeiro, Operators on Banach spaces taking compact sets inside ranges of vector measures, Proc. Amer. Math. Soc. 116 (1992), no. 4, 1031–1040. MR 1110552, DOI 10.1090/S0002-9939-1992-1110552-X
- C. Piñeiro and L. Rodríguez-Piazza, Banach spaces in which every compact lies inside the range of a vector measure, Proc. Amer. Math. Soc. 114 (1992), no. 2, 505–517. MR 1086342, DOI 10.1090/S0002-9939-1992-1086342-3
- Gilles Pisier, Factorization of linear operators and geometry of Banach spaces, CBMS Regional Conference Series in Mathematics, vol. 60, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986. MR 829919, DOI 10.1090/cbms/060
- Nicole Tomczak-Jaegermann, Banach-Mazur distances and finite-dimensional operator ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 38, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989. MR 993774
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3329-3334
- MSC: Primary 46B20; Secondary 28B05, 46G10
- DOI: https://doi.org/10.1090/S0002-9939-1995-1291790-5
- MathSciNet review: 1291790