Asymptotic type for sectorial operators and an integral of fractional powers

Nick Dungey

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    There is a standard notion of type for a sectorial linear operator acting in a Banach space. We introduce a notion of asymptotic type for a linear operator V, involving estimates on the resolvent (λI+V)⁻¹ as λ→0. We show, for example, that if V is sectorial and of asymptotic type ω then the fractional power Vα is of asymptotic type αω for a suitable range of positive α. Moreover, we establish various properties of the operator ∫₀¹dαVα ; in particular, this operator is of asymptotic type 0, for a sectorial operator V. This result has an application to the construction of operators satisfying the well-known Ritt resolvent condition.
    Original languageEnglish
    Pages (from-to)1387-1407
    Number of pages21
    JournalJournal of Functional Analysis
    Volume256
    Issue number5
    DOIs
    Publication statusPublished - 2009

    Keywords

    • sectorial operator
    • fractional power
    • type
    • Ritt resolvent condition
    • power-bounded operator

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