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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
Published electronically: September 19, 2002
MathSciNet review: 1949884
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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

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

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