Statistical linear spaces. II. Strongest -norm
We investigate the problem when the strong dual of a projective limit of (LB)-spaces coincides with the inductive limit of the strong duals. It is well-known that the answer is affirmative for spectra of Banach spaces if the projective limit is a quasinormable Fréchet space. In that case, the spectrum satisfies a certain condition which is called “strong P-type”. We provide an example which shows that strong P-type in general does not imply that the strong dual of the projective limit is the inductive...
A reflexive topological group is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group and of its dual group is reflexive. In this paper we establish an adequate concept of strong reflexivity for convergence groups. We prove that complete metrizable nuclear groups and products of countably many locally compact topological groups are BB-strongly reflexive.
Let be a real Banach space and let be an ideal of over a -finite measure space . Let be the space of all strongly -measurable functions such that the scalar function , defined by for , belongs to . The paper deals with strong topologies on . In particular, the strong topology ( the order continuous dual of ) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.