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

Aharon Atzmon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A Fréchet space with a two-sided Schauder basis is constructed, such that the corresponding bilateral shift is continuous and invertible, and has no common nontrivial invariant subspace with its inverse. This shows in particular, that the problem of existence of hyperinvariant subspaces for operators on general Fréchet spaces, admits a negative answer. It is also shown that the dual of the Fréchet space constructed can be identified with a commutative locally convex complete topological algebra with unit, which has no closed nontrivial ideals.

Original languageEnglish
Pages (from-to)68-77
Number of pages10
JournalJournal of Functional Analysis
Volume55
Issue number1
DOIs
StatePublished - Jan 1984
Externally publishedYes

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