Schauder decompositions and the Grothendieck and Dunford--Pettis properties in Köthe echelon spaces of infinite order

DOI10.1007/S11117-006-2014-1zbMath1131.46005OpenAlexW2027919460MaRDI QIDQ882823

José Bonet, Werner J. Ricker

Publication date: 24 May 2007

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-006-2014-1

zbMATH Keywords

Grothendieck spaceSchauder decompositiondensity conditionDunford--Pettis propertyKöthe echelon spaces

Mathematics Subject Classification ID

Sequence spaces (including Köthe sequence spaces) (46A45) Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Vector-valued measures and integration (46G10) 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)

\(C_{0}\)-semigroups and mean ergodic operators in a class of Fréchet spaces ⋮ Characterizing Fréchet–Schwartz spaces via power bounded operators ⋮ Isomorphic Schauder decompositions in certain Banach spaces ⋮ Mean ergodic semigroups of operators ⋮ Series representations in spaces of vector‐valued functions via Schauder decompositions ⋮ Dunford-Pettis type properties and the Grothendieck property for function spaces ⋮ Grothendieck spaces with the Dunford-Pettis property ⋮ Some permanence results of the Dunford-Pettis and Grothendieck properties in lcHs ⋮ Uniform mean ergodicity of \(C_0\)-semigroups in a class of Fréchet spaces ⋮ Grothendieck spaces: the landscape and perspectives

Cites Work

• The canonical spectral measure in Köthe echelon spaces
• Uniform convergence of operators on \(L^{\infty}\) and similar spaces
• The problem of topologies of Grothendieck for quojections
• Countable additivity of multiplicative, operator-valued set functions
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• Distinguishedness of weighted Fréchet spaces of continuous functions
• Spectral Operators of Scalar Type in Grothendieck Spaces with the Dunford-Pettis Property
• Spectral Measures, Boundedly σ-Complete Boolean Algebras and Applications to Operator Theory
• Stefan Heinrich's Density Condition for Fréchet Spaces and the Characterization of the Distinguished Köthe Echelon Spaces
• Montel subspaces of Fréchet spaces of Moscatelli type
• Spectra of Scalar-Type Spectral Operators and Schauder Decompositions
• Schauder Decompositions in (m)
• Introduction to the Theory of Bases
• Resolutions of the identity in Fréchet spaces
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