Bulletin of the Belgian Mathematical Society - Simon Stevin

On the existence of basic sequences in non-archimedean locally convex spaces

Wiesław Śliwa

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Abstract

We prove that there exist non-archimedean (n.a.) locally convex spaces without basic orthogonal sequences, and even without Schauder basic sequences. Among other things any n.a. Köthe space with the weak topology has no basic orthogonal sequence. On the other hand, we show that the strong dual of any infinite-dimensional n.a. polar Fréchet space and any n.a. LF-space have basic orthogonal sequences.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 2 (2006), 363-372.

Dates
First available in Project Euclid: 19 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1148059471

Digital Object Identifier
doi:10.36045/bbms/1148059471

Mathematical Reviews number (MathSciNet)
MR2259915

Zentralblatt MATH identifier
1143.46047

Subjects
Primary: 46S10: Functional analysis over fields other than $R$ or $C$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05] 46A35: Summability and bases [See also 46B15]

Keywords
Orthogonal basic sequence Schauder basic sequence

Citation

Śliwa, Wiesław. On the existence of basic sequences in non-archimedean locally convex spaces. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 2, 363--372. doi:10.36045/bbms/1148059471. https://projecteuclid.org/euclid.bbms/1148059471


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