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Characterization of operators taking P-summable sequences into sequences in the range of a vector measure

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영남수학회 (Youngnam Mathematical Society)|2008.03|East Asian Mathematical Journal|제24권 제2호|pp. 201-212

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참고문헌

키워드

vector measuresp-summable sequences
주제분류수학

초록

We characterize operators between Banach spaces sending unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure of bounded variation. Further, we describe operators between Banach spaces taking unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure.

Abstract

We characterize operators between Banach spaces sending unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure of bounded variation. Further, we describe operators between Banach spaces taking unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure.

참고문헌 (11)

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  3. J. Diestel, "An averaging property of the range of a vector measure", Bull. Amer. Math. Soc, 82, pp.907~909 (1976)
  4. J. Diestel, "Vector measures", AMS Surveys; no. 15, ~ (1977)
  5. J. Diestel, "Absolutely summing operators" (1995), Cambridge University Press
  6. C. Pi˜neiro, "Banach spaces in which every compact lies inside the range of a vector measure", Proc. Amer. Math. Soc, 114, pp.505~517 (1992)
  7. C. Pi˜neiro, "Operators on Banach spaces taking compact sets inside ranges of vector measures", Proc. Amer. Math. Soc, 116, pp.1031~1040 (1992)
  8. C. Pi˜neiro, "Banach spaces in which every p-weakly summable sequences lies in the range of a vector measure", Proc. Amer. Math. Soc, 124, pp.2013~2020 (1996)
  9. C. Pi˜neiro, "On p-summable sequences in the range of a vector measure", Proc. Amer. Math. Soc, 125, pp.2073~2082 (1997)
  10. L. Rodriguez-Piazza, "The range of a vector measure determines its total variation", Proc. Amer. Math. Soc, 111, pp.205~214 (1991)
  11. G. Thomas, "The Lebesgue-Nikodym theorem for vector-valued Radon measures", Mem. Amer. Math. Soc, (139) (1974)

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