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 | References | Similar Articles | Additional Information

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