Mackey compactness in Banach spaces
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- by Joe Howard
- Proc. Amer. Math. Soc. 37 (1973), 108-110
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312212-X
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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
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 117523
- A. Grothendieck, Sur les applications linéaires faiblement compactes d’espaces du type $C(K)$, Canad. J. Math. 5 (1953), 129–173 (French). MR 58866, DOI 10.4153/cjm-1953-017-4
- Walter Rudin, Principles of mathematical analysis, 2nd ed., McGraw-Hill Book Co., New York, 1964. MR 166310
- Albert Wilansky, Functional analysis, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1964. MR 170186
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 108-110
- MSC: Primary 46B05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312212-X
- MathSciNet review: 0312212