Weakly admissible H-calculus on reflexive Banach spaces

Felix L. Schwenninger*, Hans Zwart

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    3 Citations (Scopus)
    63 Downloads (Pure)


    We show that, given a reflexive Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded) functional calculus. The construction uses a Toeplitz operator and is motivated by system theory. In separable Hilbert spaces, we even get admissibility. Furthermore, it is investigated when a bounded calculus can be guaranteed. For this we introduce the new notion of exact observability by direction.
    Original languageEnglish
    Pages (from-to)796-815
    Number of pages20
    JournalIndagationes mathematicae
    Issue number4
    Publication statusPublished - Dec 2012


    • MSC-47A60
    • MSC-47B35
    • MSC-47D06
    • MSC-93C25
    • Weak admissibility
    • Operator semigroup
    • Functional calculus
    • H-infinity
    • Toeplitz operator
    • Exact observability by direction


    Dive into the research topics of 'Weakly admissible H-calculus on reflexive Banach spaces'. Together they form a unique fingerprint.

    Cite this