Nonzero fixed points of power-bounded linear operators

Efe A. Ok

    Research output: Contribution to journalArticlepeer-review

    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 Hubert space, being uniformly asymptotically regular and not strongly stable guarantees the existence of a nonzero fixed point.

    Original languageEnglish (US)
    Pages (from-to)1539-1551
    Number of pages13
    JournalProceedings of the American Mathematical Society
    Volume131
    Issue number5
    DOIs
    StatePublished - May 2003

    Keywords

    • Asymptotic regularity
    • Compact operators
    • Contractions
    • Fixed points
    • Markov operators
    • Strong stability

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

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