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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lomonosov’s invariant subspace theorem for multivalued linear operators
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by Peter Saveliev PDF
Proc. Amer. Math. Soc. 131 (2003), 825-834 Request permission


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.
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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
  • Email:
  • 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:
  • MathSciNet review: 1937420