Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Lomonosov’s invariant subspace theorem for multivalued linear operators
HTML articles powered by AMS MathViewer

by Peter Saveliev PDF
Proc. Amer. Math. Soc. 131 (2003), 825-834 Request permission

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
Similar Articles
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: 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