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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- 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
- © 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