Sequences in the range of a vector measure with bounded variation

Author:
Cándido Piñeiro

Journal:
Proc. Amer. Math. Soc. **123** (1995), 3329-3334

MSC:
Primary 46B20; Secondary 28B05, 46G10

MathSciNet review:
1291790

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Abstract: Let *X* be a Banach space. We consider sequences 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 -valued measure of bounded variation.

**[AD]**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****[DU]**J. Diestel and J. J. Uhl Jr.,*Vector measures*, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical Surveys, No. 15. MR**0453964****[P1]**Albrecht Pietsch,*Quasinukleare Abbildungen in normierten Räumen*, Math. Ann.**165**(1966), 76–90 (German). MR**0198253****[P2]**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****[Pñ]**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**, 10.1090/S0002-9939-1992-1110552-X**[PR]**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**, 10.1090/S0002-9939-1992-1086342-3**[Ps]**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****[T]**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**

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1291790-5

Article copyright:
© Copyright 1995
American Mathematical Society