An example of a nuclear Fréchet space without the bounded approximation property

DOI10.1007/BF01175629zbMath0488.46002MaRDI QIDQ1166057

Dietmar Vogt

Publication date: 1983

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173281

zbMATH Keywords

nuclear Fréchet space without basisnuclear Fréchet space without the bounded approximation property

Mathematics Subject Classification ID

Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) 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 (10)

Unbounded linear operators and nuclear Köthe quotients ⋮ Characterization of nuclear Fréchet spaces in which every bounded set is polar ⋮ Batalin-Vilkovisky formalism in the functional approach to classical field theory ⋮ A nuclear Fréchet space consisting of 𝐶^{∞}-functions and failing the bounded approximation property ⋮ Nuclear Fréchet spaces without the bounded approximation property ⋮ Every non-normable non-archimedean Köthe space has a quotient without the bounded approximation property ⋮ Shrinking and boundedly complete Schauder frames in Fréchet spaces ⋮ Examples of non-archimedean nuclear Fréchet spaces without a Schauder basis ⋮ On tame pairs of Fréchet spaces ⋮ Continuous norms on locally convex strict inductive limit spaces

Cites Work

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• Modified construction of nuclear Frechet spaces without basis
• The structure of nuclear Frechet spaces
• Fréchet spaces with quotients failing the bounded approximation property
• Produits tensoriels topologiques et espaces nucléaires
• Nuclear Fréchet spaces without the bounded approximation property

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