Lomonosov’s invariant subspace theorem for multivalued linear operators
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- by Peter Saveliev
- Proc. Amer. Math. Soc. 131 (2003), 825-834
- DOI: https://doi.org/10.1090/S0002-9939-02-06598-X
- Published electronically: June 12, 2002
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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 $K\neq 0,$ 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.References
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Bibliographic 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
- Email: saveliev@member.ams.org
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 825-834
- MSC (2000): Primary 47A15, 47A06; Secondary 46A32, 54C60
- DOI: https://doi.org/10.1090/S0002-9939-02-06598-X
- MathSciNet review: 1937420