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Spaces of operators between Fréchet spaces

Published online by Cambridge University Press:  24 October 2008

José Bonet  and
Mikael Lindström
José Bonet
Affiliation:
Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain
Mikael Lindström
Affiliation:
Department of Mathematics, Åbo Akademi, SF-20500 Åbo, Finland
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Abstract

Motivated by recent results on the space of compact operators between Banach spaces and by extensions of the Josefson–Nissenzweig theorem to Fréchet spaces, we investigate pairs of Fréchet spaces (E, F) such that every continuous linear map from E into F is Montel, i.e. it maps bounded subsets of E into relatively compact subsets of F. As a consequence of our results we characterize pairs of Köthe echelon spaces (E, F) such that the space of Montel operators from E into F is complemented in the space of all continuous linear maps from E into F.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 1 , January 1994 , pp. 133 - 144
Copyright
Copyright © Cambridge Philosophical Society 1994

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