$H^\infty $ calculus and dilatations
摘要
We characterise the boundedness of the H calculus of a sectorial operator in terms of dilation theorems. We show e. g. that if -A generates a bounded analytic C 0 semigroup (Tt) on a UMD space, then the H calculus of A is bounded if and only if (Tt) has a dilation to a bounded group on L 2 ([0, 1], X). This generalises a Hilbert space result of C. Le Merdy. If X is an L p space we can choose another L p space in place of L 2 ([0, 1], X).
引用本文（GB/T 7714）
Andreas M. Fröhlich, Lutz Weis. $H^\infty $ calculus and dilatations[J]. Bulletin de la Société mathématique de France, 2006.
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