Geodesic
Strong duals of projective limits of (LB)-spaces
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 295-307 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46A08, 46A13, 46A20, 46M15
Keywords: derived projective limit functor; Retakh’s condition; weakly acyclic (LF)-spaces 
@article{CMJ_2002_52_2_a4,
     author = {Bonet, J. and Dierolf, S. and Wengenroth, J.},
     title = {Strong duals of projective limits of {(LB)-spaces}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {295--307},
     year = {2002},
     volume = {52},
     number = {2},
     mrnumber = {1905436},
     zbl = {1075.46501},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a4/}
}
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Bonet, J.; Dierolf, S.; Wengenroth, J. Strong duals of projective limits of (LB)-spaces. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 295-307. http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a4/