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Proceedings of the American Mathematical Society

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

 

 

On quasinilpotent operators


Authors: Il Bong Jung, Eungil Ko and Carl Pearcy
Journal: Proc. Amer. Math. Soc. 131 (2003), 2121-2127
MSC (2000): Primary 47A15
Published electronically: February 5, 2003
MathSciNet review: 1963758
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Abstract: In this note we modify a new technique of Enflo for producing hyperinvariant subspaces to obtain a much improved version of his ``two sequences'' theorem with a somewhat simpler proof. As a corollary we get a proof of the ``best'' theorem (due to V. Lomonosov) known about hyperinvariant subspaces for quasinilpotent operators that uses neither the Schauder-Tychonoff fixed point theorem nor the more recent techniques of Lomonosov.


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Additional Information

Il Bong Jung
Affiliation: Department of Mathematics, Kyungpook National University, Taegu 702-701, Korea
Email: ibjung@kyungpook.ac.kr

Eungil Ko
Affiliation: Department of Mathematics, Ewha Women’s University, Seoul 120-750, Korea
Email: eiko@mm.ewha.ac.kr

Carl Pearcy
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: pearcy@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06895-3
Keywords: Invariant subspaces, Enflo technique, extremal vectors
Received by editor(s): February 6, 2002
Published electronically: February 5, 2003
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society