A problem on the structure of Fréchet spaces

DOI10.5052/RACSAM.2010.26zbMath1262.46001OpenAlexW372365014MaRDI QIDQ549583

José Bonet

Publication date: 18 July 2011

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5052/racsam.2010.26

zbMATH Keywords

Fréchet spacesbounded operatorshypercyclic operatorschaotic operators

Mathematics Subject Classification ID

Locally convex Fréchet spaces and (DF)-spaces (46A04) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Topological algebras of operators (46H35) Cyclic vectors, hypercyclic and chaotic operators (47A16)

Related Items (4)

Power bounded weighted composition operators on function spaces defined by local properties ⋮ Closed universal subspaces of spaces of~infinitely differentiable functions ⋮ Topologizable and power bounded weighted composition operators on spaces of distributions ⋮ Generic distributional chaos and principal measure in linear dynamics

Cites Work

• A class of Banach spaces with few non-strictly singular operators
• Linear chaos
• Operators with dense, invariant, cyclic vector manifolds
• Hypercyclic operators on non-normable Fréchet spaces
• Banach spaces with small spaces of operators
• Existence of hypercyclic operators on topological vector spaces
• Frequent hypercyclicity, chaos, and unconditional Schauder decompositions
• Rotations of hypercyclic and supercyclic operators
• Banach spaces without local unconditional structure
• A new dichotomy for Banach spaces
• The Unconditional Basic Sequence Problem
• STRICTLY SINGULAR, NON-COMPACT OPERATORS EXIST ON THE SPACE OF GOWERS AND MAUREY
• A Banach Space which Admits No Chaotic Operator
• Complemented subspaces in tame power series spaces
• On hypercyclic operators on Banach spaces
• Universal families and hypercyclic operators
• Spaces of operators between Fréchet spaces
• TRANSITIVE AND HYPERCYCLIC OPERATORS ON LOCALLY CONVEX SPACES
• CHAOS FOR BACKWARD SHIFT OPERATORS
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