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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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Series that converge on sets of null density
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by R. Estrada and R. P. Kanwal PDF
Proc. Amer. Math. Soc. 97 (1986), 682-686 Request permission

Abstract:

It is shown that a series of positive terms that converges on all sets of null density should be convergent. Using this result we construct examples of complete topological vector spaces that are proper subspaces of a Banach space, but whose dual spaces coincide with the dual space of the Banach space.
References
  • Sterling K. Berberian, Lectures in functional analysis and operator theory, Graduate Texts in Mathematics, No. 15, Springer-Verlag, New York-Heidelberg, 1974. MR 0417727
  • 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
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 97 (1986), 682-686
  • MSC: Primary 40A05; Secondary 46A45
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0845987-0
  • MathSciNet review: 845987