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
Full-text PDF Free Access
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.
- Sterling K. Berberian, Lectures in functional analysis and operator theory, Springer-Verlag, New York-Heidelberg, 1974. Graduate Texts in Mathematics, No. 15. 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
S. K. Berberian, Lectures in functional analysis and operator theory, Springer-Verlag, New York, 1974.
J. L. Kelley and I. Namioka, Linear topological spaces, Van Nostrand, Princeton, N.J., 1963.