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Lomonosov's invariant subspace theorem for multivalued linear operators

Author: Peter Saveliev
Journal: Proc. Amer. Math. Soc. 131 (2003), 825-834
MSC (2000): Primary 47A15, 47A06; Secondary 46A32, 54C60
Published electronically: June 12, 2002
MathSciNet review: 1937420
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Abstract: The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator $T$ on an infinite-dimensional normed space $E$ ``commutes'' with a compact operator $K\neq0,$ i.e., $TK=KT,$ then $T$ has a non-trivial closed invariant subspace. We generalize this theorem for multivalued linear operators. We also provide an application to single-valued linear operators.

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Additional Information

Peter Saveliev
Affiliation: Department of Mathematics, Allegheny College, Meadville, Pennsylvania 16335
Address at time of publication: Department of Mathematics, Marshall University, Huntington, West Virginia 25755-2560

Keywords: Invariant subspace, Lomonosov's theorem, multivalued map, linear relation
Received by editor(s): September 19, 2000
Received by editor(s) in revised form: October 14, 2001
Published electronically: June 12, 2002
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society