A Banach space with a symmetric basis which contains no or , and all its symmetric basic sequences are equivalent
In this note we present an affirmative answer to the problem posed by M. Baronti and C. Franchetti (oral communication) concerning a characterization of Lp-spaces among Orlicz sequence spaces. In fact, we show a more general characterization of Orlicz spaces isometric to Lp-spaces.
The equivalence of the two following properties is proved for every Banach lattice :1) is weakly sequentially complete.2) Every -Borel measurable linear functional on is -continuous.
We characterize when weighted -spaces of holomorphic functions have the dual density condition, when the weights are radial and grow logarithmically.
In this article we give some properties of the tensor product, with the and topologies, of two locally convex spaces. As a consequence we prove that the theory of M. de Wilde of the closed graph theorem does not contain the closed graph theorem of L. Schwartz.