Nonzero fixed points of power-bounded linear operators

Ok, Efe

doi:10.1090/S0002-9939-02-06740-0

Nonzero fixed points of power-bounded linear operators
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by Efe A. Ok PDF

Proc. Amer. Math. Soc. 131 (2003), 1539-1551 Request permission

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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