Modified construction of nuclear Frechet spaces without basis

DOI10.1016/0022-1236(76)90066-5zbMath0339.46004OpenAlexW2030658140MaRDI QIDQ1231258

Boris S. Mityagin, Plamen Djakov

Publication date: 1976

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(76)90066-5

Mathematics Subject Classification ID

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

Related Items (11)

Subspaces without bases in nuclear Frechet spaces ⋮ Existence of continuable bases in spaces of functions, analytic in compacta ⋮ Basis in the space of \(C^\infty\)-functions on a graduated sharp cusp ⋮ Closed ideals of \(A^\infty\) and a famous problem of Grothendieck ⋮ On bounded approximation properties of spaces of holomorphic functions on certain open subsets of strong duals of nuclear Frechet spaces ⋮ An example of a nuclear Fréchet space without the bounded approximation property ⋮ Complemented basic sequences in nuclear Frechet spaces with finite dimensional decompositions ⋮ Generalization of a theorem of Bohr for bases in spaces of holomorphic functions of several complex variables ⋮ 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 ⋮ Bases in the spaces of Whitney jets ⋮ Superspaces of (s) with strong finite dimensional decomposition

Cites Work

• Examples of nuclear linear metric spaces without a basis
• Über die Einbettung der nuklearen Räume in \((s)^ A\)
• Perfect Fréchet spaces
• APPROXIMATE DIMENSION AND BASES IN NUCLEAR SPACES
• Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basic
• On the isomorphism of cartesian products of locally convex spaces
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