Series that converge on sets of null density
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. © 1986 American Mathematical Society.
Publication Source (Journal or Book title)
Proceedings of the American Mathematical Society
Estrada, R., & Kanwal, R. (1986). Series that converge on sets of null density. Proceedings of the American Mathematical Society, 97 (4), 682-686. https://doi.org/10.1090/S0002-9939-1986-0845987-0