Examples of non-archimedean nuclear Fréchet spaces without a Schauder basis

DOI10.1016/S0019-3577(00)80029-4zbMath1016.46047OpenAlexW2147108515MaRDI QIDQ5951551

Wiesław Śliwa

Publication date: 28 January 2003

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0019-3577(00)80029-4

zbMATH Keywords

Schauder basis\(p\)-adic functional analysis

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Locally convex Fréchet spaces and (DF)-spaces (46A04) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Summability and bases in topological vector spaces (46A35)

Related Items (6)

The finite-dimensional decomposition property in non-Archimedean Banach spaces ⋮ On closed subspaces of non-Archimedean nuclear Fréchet spaces with a Schauder basis ⋮ Every non-normable non-archimedean Köthe space has a quotient without the bounded approximation property ⋮ On Topological Classification of Non-Archimedean Fréchet Spaces ⋮ Closed subspaces without Schauder bases in non-Archimedean Fréchet spaces ⋮ On closed subspaces with Schauder bases in non-archimedean Fréchet spaces

Cites Work

• An example of a nuclear Fréchet space without the bounded approximation property
• Orthogonal sequences in non-Archimedean locally convex spaces
• Every infinite-dimensional non-Archimedean Fréchet space has an orthogonal basic sequence
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