In this paper it is proved that if and are two sequences of infinite-dimensional Banach spaces then is not -complete. If and are also reflexive spaces there is on a separated locally convex topology , coarser than the initial one, such that is a bornological barrelled space which is not an inductive limit of Baire spaces. It is given also another results on -completeness and bornological spaces.
It is shown that on strongly pseudoconvex domains the Bergman projection maps a space of functions growing near the boundary like some power of the Bergman distance from a fixed point into a space of functions which can be estimated by the consecutive power of the Bergman distance. This property has a local character. Let Ω be a bounded, pseudoconvex set with C³ boundary. We show that if the Bergman projection is continuous on a space defined by weighted-sup seminorms and equipped with the topology...
Let be a -algebra on a set . If belongs to let be the characteristic function of . Let be the linear space generated by endowed with the topology of the uniform convergence. It is proved in this paper that if is an increasing sequence of subspaces of covering it, there is a positive integer such that is a dense barrelled subspace of , and some new results in measure theory are deduced from this fact.