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Bounded linear maps between (LF)-spaces.

Angela A. Albanese — 2003

RACSAM

Characterizations of pairs (E,F) of complete (LF)?spaces such that every continuous linear map from E to F maps a 0?neighbourhood of E into a bounded subset of F are given. The case of sequence (LF)?spaces is also considered. These results are similar to the ones due to D. Vogt in the case E and F are Fréchet spaces. The research continues work of J. Bonet, A. Galbis, S. Önal, T. Terzioglu and D. Vogt.

Representations of the spaces C ( N ) H k , p ( N )

A. AlbaneseV. Moscatelli — 2000

Studia Mathematica

We give a representation of the spaces C ( N ) H k , p ( N ) as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that C ( N ) H k , 2 ( N ) is isomorphic to the sequence space s l 2 ( l 2 ) , thereby showing that the isomorphy class does not depend on the dimension N if p=2.

Characterizing Fréchet-Schwartz spaces via power bounded operators

Angela A. AlbaneseJosé BonetWerner J. Ricker — 2014

Studia Mathematica

We characterize Köthe echelon spaces (and, more generally, those Fréchet spaces with an unconditional basis) which are Schwartz, in terms of the convergence of the Cesàro means of power bounded operators defined on them. This complements similar known characterizations of reflexive and of Fréchet-Montel spaces with a basis. Every strongly convergent sequence of continuous linear operators on a Fréchet-Schwartz space does so in a special way. We single out this type of "rapid convergence" for a sequence...

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