An operator on a Fréchet space with no common invariant subspace with its inverse

DOI10.1016/0022-1236(84)90019-3zbMath0552.47006OpenAlexW2066378431MaRDI QIDQ801521

Aharon Atzmon

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0022-1236(84)90019-3

zbMATH Keywords

Schauder basisformal Laurent seriesFréchet-Montel spacecommon invariant subspaceexistence of hyperinvariant subspacesoperators of formal multiplication

Mathematics Subject Classification ID

Sequence spaces (including Köthe sequence spaces) (46A45) Invariant subspaces of linear operators (47A15) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Summability and bases in topological vector spaces (46A35) Ideals and subalgebras (46H10)

Related Items (5)

Countable inductive limits of Fréchet algebras ⋮ Convolution equations in spaces of sequences with an exponential growth constraint ⋮ Reducible representations of abelian groups ⋮ Invariant subspaces of operator algebras ⋮ Asymptotically holomorphic functions and translation invariant subspaces of weighted Hilbert spaces of sequences

Cites Work

• Operators which are annihilated by analytic functions and invariant subspaces
• The invariant subspaces of the continuous endomorphisms on \(\omega\)
• The 𝐻^{𝑝} spaces of an annulus
• A note on invariant subspaces
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