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A normability condition on locally convex spaces.

S. Önal, T. Terzioglu (1991)

Revista Matemática de la Universidad Complutense de Madrid

In a previous work (1990) we introduced a certain property (y) on locally convex spaces and used it to remove the assumption of separability from the theorem of Bellenot and Dubinsky on the existence of nuclear Köthe quotients of Fréchet spaces. Our purpose is to examine condition (y) further and relate it to some other normability conditions. Some of our results were already announced in Önal (1989).

A uniform boundedness principle of Pták

Charles W. Swartz (1993)

Commentationes Mathematicae Universitatis Carolinae

The Antosik-Mikusinski Matrix Theorem is used to give an extension of a uniform boundedness principle due to V. Pták to certain metric linear spaces. An application to bilinear operators is given.

Bounded linear maps between (LF)-spaces.

Angela A. Albanese (2003)


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.

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