Nonzero fixed points of power-bounded linear operators

Author:
Efe A. Ok

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1539-1551

MSC (2000):
Primary 47H09, 47H10; Secondary 47B07

DOI:
https://doi.org/10.1090/S0002-9939-02-06740-0

Published electronically:
September 19, 2002

MathSciNet review:
1949884

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper provides a variety of sufficient conditions for the existence of a nonzero fixed point of a power-bounded linear operator defined on a real Banach space. In the case of power-bounded positive operators on a Banach lattice, among the conditions we provide are not being strongly stable along with commuting with a compact operator or being quasicompact. These results apply directly to Markov operators. In the case of an arbitrary power-bounded operator on a Hilbert space, being uniformly asymptotically regular and not strongly stable guarantees the existence of a nonzero fixed point.

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Additional Information

**Efe A. Ok**

Affiliation:
Department of Economics, New York University, 269 Mercer St., New York, New York 10003

Email:
efe.ok@nyu.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06740-0

Keywords:
Fixed points,
contractions,
compact operators,
Markov operators,
strong stability,
asymptotic regularity

Received by editor(s):
October 29, 2001

Received by editor(s) in revised form:
December 17, 2001

Published electronically:
September 19, 2002

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2002
American Mathematical Society