Journal of Operator Theory

Volume 40, Issue 2, Fall 1998 pp. 409-417.

A new Lomonosov lemma

Authors: Bernard Chevreau (1), Wing Suet Li (2), and Carl Pearcy (3)
Author institution: (1) Universite de Bordeaux, U.F.R. de Mathematiques, 33405 Talence, France
(2) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.
(3) Department of Mathematics, Texas A&M University, College Station, TX 77843, U.S.A.

Summary: In 1973 V. Lomonosov obtained a beautiful result on the existence of nontrivial invariant subspaces for compact-related operators on Banach space. The key idea has become known as ``Lomonosov's lemma''. Since then, generalizations have been obtained by various authors. In this note we give more elementary proofs for the main theorems from [8] (and [4]), including a ``new'' Lomonosov-type lemma. This allows us to generalize earlier work in this area.

Keywords: Invariant subspaces, transitive algebras, Lomonosov lemma

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