An operator without invariant subspaces on a nuclear Fréchet space

DOI10.2307/2007039zbMath0553.47002OpenAlexW2115623113WikidataQ56391020 ScholiaQ56391020MaRDI QIDQ802121

Aharon Atzmon

Publication date: 1983

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2007039

zbMATH Keywords

invariant subspacedual spacebackward shiftnuclear Fréchet spaceclosed nontrivial idealsnuclear countably Hilbert space

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) 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) Ideals and subalgebras (46H10)

Related Items (14)

Positive answer to the invariant and hyperinvariant subspaces problems for hyponormal operators ⋮ The invariant subspace problem for non-Archimedean Köthe spaces ⋮ A model for operators with cyclic adjoint ⋮ Countable inductive limits of Fréchet algebras ⋮ On certain open problems in topological algebras ⋮ Invariant subspace problem for classical spaces of functions ⋮ Invariant subspaces for non-normable Fréchet spaces ⋮ The invariant subspace problem for the space of smooth functions on the real line ⋮ Invariant subspaces of operator algebras ⋮ Hypercyclic operators on non-normable Fréchet spaces ⋮ Invariant subspaces for Fréchet spaces without continuous norm ⋮ An overview of some recent developments on the Invariant Subspace Problem ⋮ Un opérateur sans sous-espace invariant: Simplification de l'exemple de P. Enflo ⋮ Asymptotically holomorphic functions and translation invariant subspaces of weighted Hilbert spaces of sequences

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