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Non-Archimedean t-Frames and FM-Spaces

Published online by Cambridge University Press:  20 November 2018

N. De Grande-De Kimpe ,
C. Perez-Garcia  and
W. H. Schikhof
N. De Grande-De Kimpe
Affiliation:
Department of Mathematics Vrije Universiteit Brussel Pleinlaan 2 (10F7) B 1050 Brussels Belgium
C. Perez-Garcia
Affiliation:
Department of Mathematics Falcutad de Ciencias Universidad de Cantabria 39071 Santander Spain
W. H. Schikhof
Affiliation:
Mathematisch instituut Katholieke Universiteit Toernooiveld, 6525 ED Nijmegen The Netherlands
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Abstract

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We generalize the notion of t-orthogonality in p-adic Banach spaces by introducing t-frames (§2). This we use to prove that a Fréchet-Montel (FM-)space is of countable type (Theorem 3.1), the non-archimedeancounterpart of a well known theorem in functional analysis over ℝ or ℂ ([6], p. 231). We obtain several characterizations of FM-spaces (Theorem 3.3) and characterize the nuclear spaces among them (§4).

Keywords

46S10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 475 - 483
Copyright
Copyright © Canadian Mathematical Society 1992

References

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