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Proceedings of the American Mathematical Society

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Mackey compactness in Banach spaces


Author: Joe Howard
Journal: Proc. Amer. Math. Soc. 37 (1973), 108-110
MSC: Primary 46B05
MathSciNet review: 0312212
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Abstract: If $ A'$, a subset of a conjugate Banach space $ X'$, is sequentially compact in the Mackey topology $ (\tau (X',X))$, then $ A'$ is conditionally compact in the Mackey topology. The converse is not true.


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

  • [1] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • [2] A. Grothendieck, Sur les applications linéaires faiblement compactes d’espaces du type 𝐶(𝐾), Canadian J. Math. 5 (1953), 129–173 (French). MR 0058866
  • [3] Walter Rudin, Principles of mathematical analysis, Second edition, McGraw-Hill Book Co., New York, 1964. MR 0166310
  • [4] Albert Wilansky, Functional analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR 0170186

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0312212-X
Keywords: Mackey topology, conditionally compact, sequentially compact
Article copyright: © Copyright 1973 American Mathematical Society