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An operator not satisfying Lomonosov's hypothesis

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
38
Issue
3
Identifiers
DOI: 10.1016/0022-1236(80)90073-7
Disciplines
  • Mathematics

Abstract

Abstract An example is presented of a Hilbert space operator such that no non-scalar operator that commutes with it commutes with a non-zero compact operator. This shows that Lomonosov's invariant subspace theorem does not apply to every operator.

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