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Strong duals of projective limits of (LB)-spaces

J. Bonet, Susanne Dierolf, J. Wengenroth (2002)

Czechoslovak Mathematical Journal

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...

Strong reflexivity of Abelian groups

Montserrat Bruguera, María Jesús Chasco (2001)

Czechoslovak Mathematical Journal

A reflexive topological group G is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group G 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.

Strong topologies on vector-valued function spaces

Marian Nowak (2000)

Czechoslovak Mathematical Journal

Let ( X , · X ) be a real Banach space and let E be an ideal of L 0 over a σ -finite measure space ( Ø , Σ , μ ) . Let ( X ) be the space of all strongly Σ -measurable functions f Ø X such that the scalar function f ˜ , defined by f ˜ ( ø ) = f ( ø ) X for ø Ø , belongs to E . The paper deals with strong topologies on E ( X ) . In particular, the strong topology β ( E ( X ) , E ( X ) n ) ( E ( X ) n = the order continuous dual of E ( X ) ) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.

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