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Proceedings of the American Mathematical Society

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Series that converge on sets of null density

Authors: R. Estrada and R. P. Kanwal
Journal: Proc. Amer. Math. Soc. 97 (1986), 682-686
MSC: Primary 40A05; Secondary 46A45
MathSciNet review: 845987
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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.

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  • [1] Sterling K. Berberian, Lectures in functional analysis and operator theory, Springer-Verlag, New York-Heidelberg, 1974. Graduate Texts in Mathematics, No. 15. MR 0417727
  • [2] J. L. Kelley and Isaac Namioka, Linear topological spaces, 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. The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. MR 0166578

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Article copyright: © Copyright 1986 American Mathematical Society