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Weak convergence and weak compactness in abstract $ M$ spaces


Authors: Shu Tao Chen and Hui Ying Sun
Journal: Proc. Amer. Math. Soc. 123 (1995), 1441-1447
MSC: Primary 46B42; Secondary 54E18
DOI: https://doi.org/10.1090/S0002-9939-1995-1273482-1
MathSciNet review: 1273482
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Abstract: This paper presents some properties of bounded linear functionals on $ \sigma $ complete abstract M spaces, from which some criteria for weak convergence and weak compactness in such spaces are obtained.


References [Enhancements On Off] (What's this?)

  • [1] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. II, Springer-Verlag, Berlin and New York, 1979. MR 540367 (81c:46001)
  • [2] W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces. I, North-Holland, Amsterdam and London, 1971.
  • [3] A. C. Zaanen, Riesz spaces. II, North-Holland, Amsterdam, New York, and Oxford, 1983. MR 704021 (86b:46001)
  • [4] L. V. Kantorovitch, B. Z. Vulih, and A. G. Pinsker, Functional analysis in partially order spaces, Gosudarstr, Izdat. Tehn. Teor. Lit., Moscow and Leningrad, 1950. (Russian) MR 0038006 (12:340d)
  • [5] K. Yosida, Functional analysis, Springer-Verlag, Berlin and New York, 1978. MR 0500055 (58:17765)
  • [6] J. Diestel, Sequences and series in Banach spaces, Springer-Verlag, Berlin and New York, 1984. MR 737004 (85i:46020)
  • [7] A. Wilansky, Modern methods in topological vector spaces, McGraw-Hill, New York, 1987.
  • [8] N. Dunford and J. T. Schwartz, Linear operators, Interscience, New York, 1958.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1273482-1
Keywords: Banach lattice, abstract M spaces, weak convergence, weak compactness, extreme point
Article copyright: © Copyright 1995 American Mathematical Society

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