A characterization of totally reflexive Fréchet spaces

DOI10.1007/BF01215650zbMath0683.46008MaRDI QIDQ1824817

Manuel Valdivia

Publication date: 1989

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

Full work available at URL: https://eudml.org/doc/174012

zbMATH Keywords

construction of a Schauder basis of a certain type for a suitable quotientDavis-Figiel-Johnson-Pełczyński factorization theorem for weakly compact operatorsproblem of Grothendieckprojective limit of a sequence of reflexive Banach spacesquotients with a Schauder basisSchauder basis with property Pseparated quotienttotally reflexive Fréchet spacesweakly compact projective limits

Mathematics Subject Classification ID

Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) 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) Duality theory for topological vector spaces (46A20) Inductive and projective limits in functional analysis (46M40) Summability and bases in topological vector spaces (46A35) Reflexivity and semi-reflexivity (46A25)

Related Items (9)

The density condition in subspaces and quotients of Fréchet spaces ⋮ Operator spaces containing \(c_ 0\) or \(\ell_ \infty\) ⋮ On quotients of Köthe sequence spaces of infinite order ⋮ (LF) ‐ Spaces and Tensor Products ⋮ Basic Sequences in the Dual of a Fréchet Space ⋮ Fréchet spaces with no infinite-dimensional Banach quotients ⋮ Bases and quasi-reflexivity in Fréchet spaces ⋮ Intersections of Fréchet spaces and (LB)-spaces ⋮ On Some Problems of Grothendieck Concerning (F) and (DF) Spaces

Cites Work

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• Completeness and Compactness in Linear Topological Spaces

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