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A Question of Valdivia on Quasinormable Fréchet Spaces

Published online by Cambridge University Press:  20 November 2018

José Bonet
José Bonet*
Affiliation:
Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain
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Abstract

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It is proved that a Fréchet space is quasinormable if and only if every null sequence in the strong dual converges equicontinuously to the origin. This answers positively a question raised by Valdivia. As a consequence a positive answer to a problem of Jarchow on Fréchet Schwartz spaces is obtained.

Keywords

46A0646A12
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 301 - 304
Copyright
Copyright © Canadian Mathematical Society 1991

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