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

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
55
Issue
1
Identifiers
DOI: 10.1016/0022-1236(84)90019-3
Disciplines
  • Mathematics

Abstract

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.

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