Examples of nuclear linear metric spaces without a basis

DOI10.1007/BF01075487zbMath0344.46014MaRDI QIDQ1232775

N. M. Zobin, Boris S. Mityagin

Publication date: 1974

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Mathematics Subject Classification ID

General theory of locally convex spaces (46A03) Summability and bases in topological vector spaces (46A35)

Related Items

Logarithmic dimension and bases in Whitney spaces ⋮ Basis in the space of \(C^\infty\)-functions on a graduated sharp cusp ⋮ On bounded approximation properties of spaces of holomorphic functions on certain open subsets of strong duals of nuclear Frechet spaces ⋮ Some remarks on quasi-equivalence of bases in Fréchet spaces ⋮ Modified construction of nuclear Frechet spaces without basis ⋮ Nuclear Frechet spaces without bases. III: Every nuclear Frechet space not isomorphic to omega admits a subspace and a quotient space without a strong finite dimensional decomposition

Cites Work

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• The absence of a linear resolvent operator in problems in the theory of holomorphic functions
• A counterexample to the approximation problem in Banach spaces
• APPROXIMATE DIMENSION AND BASES IN NUCLEAR SPACES
• Nukleare Funktionenräume und singuläre elliptische Differentialoperatoren
• The Approximation Problem for Banach Spaces
• Produits tensoriels topologiques et espaces nucléaires

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