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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Compactness of sets of integrable functions with values in a Banach space
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by Atle Seierstad PDF
Proc. Amer. Math. Soc. 52 (1975), 204-208 Request permission

Abstract:

The present paper gives direct proofs of compactness (in a pairing topology) of bounded sets of strongly integrable functions with values in weakly compact subsets of a Banach space. The pairing in question is that one defined by the integral of the scalar product of two strongly integrable functions with values in the Banach space and its dual, respectively.
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 0117523
  • J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. MR 0166578
  • A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag New York, Inc., New York, 1969. MR 0276438
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 204-208
  • MSC: Primary 46E40; Secondary 46G99
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0470676-7
  • MathSciNet review: 0470676