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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

1. De Grande-De Kimpe, N., Perfect locally K-convex sequence spaces, Proc. Kon. Ned. Akad. v. Wet. A 74(1971), 471–482.Google Scholar
2. De Grande-De Kimpe, N., On spaces of operators between locally K-convex spaces, Proc. Kon. Ned. Akad. v. Wet. A 75(1972), 113–129.Google Scholar
3. De Grande-De Kimpe, N., Non-archimedeanFréchet spaces generalizing spaces ofanalytic functions, Proc. Kon. Ned. Akad. v. Wet. A 85(1982), 423–139.Google Scholar
4. De Grande-De Kimpe, N., Non-archimedean topologies of countable type and associated operators, Proc. Kon. Ned. Akad. v. Wet. A 90(1987), 15–28.Google Scholar
5. De Grande-De Kimpe, N., Nuclear topologies on non-archimedean locally convex spaces, Proc. Kon. Ned. Akad. v. Wet. A 90(1987), 279–292.Google Scholar
6. Jarchow, H., Locally convex spaces, Teubner, Stuttgart, (1981 ).Google Scholar
7. Schikhof, W. H., Locally convex spaces over non-spheric ally complete fields I-II, Bull Soc. Math. Belgique, (B) XXXVIII (1986), 187–224.Google Scholar
8. Schikhof, W. H., P-adic nonconvexcompactoids, Proc. Kon Ned. Akad. v. Wet. A 92(1989), 339–342.Google Scholar
9. Schikhof, W. H. and van Rooij, A. C. M., Seven papers on p-adic analysis, Report 9125, Math. Inst. Katholieke Universiteit, Nijmegen, (1991).Google Scholar
10. Van Rooij, A. C. M., Notes on p-adic Banach spaces, Reports 7633 and 7725, Math. Inst. Katholieke Universiteit, Nijmegen (1976,1977).Google Scholar
11. Van Rooij, A. C. M., Non-archimedean Functional Analysis, Marcel Dekker, New York, (1978).Google Scholar