Nonzero fixed points of power-bounded linear operators

Ahmet Ok

    Research output: Contribution to journalArticle

    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

    Fingerprint

    Banach spaces
    Bounded Linear Operator
    Mathematical operators
    Power Bounded Operator
    Fixed point
    Markov Operator
    Banach Lattice
    Hubert Space
    Positive Operator
    Compact Operator
    Bounded Operator
    Banach space
    Sufficient Conditions
    Arbitrary

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    Nonzero fixed points of power-bounded linear operators. / Ok, Ahmet.

    In: Proceedings of the American Mathematical Society, Vol. 131, No. 5, 05.2003, p. 1539-1551.

    Research output: Contribution to journalArticle

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