Functional calculus for C 0 -groups using type and cotype

Jan Rozendaal*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    We study the functional calculus properties of generators of C 0 -groups under type and cotype assumptions on the underlying Banach space. In particular, we show the following. Let -iA generate a C 0 -group on a Banach space X with type p∈[1, 2] and cotype q ∈ [2,∞). Then f(A):(X,D(A)) 1p-1q,1 → X is bounded for each bounded holomorphic function f on a sufficiently large strip. As a corollary of this result, for sectorial operators, we quantify the gap between bounded imaginary powers and a bounded ℋ -calculus in terms of the type and the cotype of the underlying Banach space. For cosine functions, we obtain similar results as for C 0 -groups. We extend our theorems to R-bounded operator-valued calculi, and we give an application to the theory of rational approximation of C 0 -groups.

    Original languageEnglish
    Pages (from-to)17-47
    Number of pages31
    JournalQuarterly Journal of Mathematics
    Issue number1
    Publication statusPublished - 1 Mar 2019


    Dive into the research topics of 'Functional calculus for C 0 -groups using type and cotype'. Together they form a unique fingerprint.

    Cite this