Strong duals of projective limits of (LB)-spaces |
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Authors: | J. Bonet S. Dierolf J. Wengenroth |
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Affiliation: | (1) Departamento de Matematica Aplicada, E.T.S. Arquitectura, Universidad PolitÉcnica de Valencia, E–46071 Valencia, Spain;(2) FB IV—Mathematik, Universität Trier, D–54286 Trier, Germany |
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Abstract: | 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 limit of the strong duals, but on the other hand we show that this is indeed true if one deals with projective spectra of retractive (LB)-spaces. Finally, we apply our results to a question of Grothendieck about biduals of (LF)-spaces. |
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Keywords: | derived projective limit functor Retakh's condition weakly acyclic (LF)-spaces |
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