Isometric dilations and 𝐻^{∞} calculus for bounded analytic semigroups and Ritt operators
| Autor: | Christian Le Merdy, Stephan Fackler, Cédric Arhancet |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Semigroup Applied Mathematics General Mathematics 010102 general mathematics Amenable group Banach space medicine.disease 01 natural sciences Group representation Dilation (operator theory) Functional calculus Bounded function 0103 physical sciences medicine 010307 mathematical physics 0101 mathematics Calculus (medicine) Mathematics |
| Zdroj: | Transactions of the American Mathematical Society. 369:6899-6933 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran/6849 |
| Popis: | We show that any bounded analytic semigroup on L p L^p (with 1 > p > ∞ 1>p>\infty ) whose negative generator admits a bounded H ∞ ( Σ θ ) H^{\infty }(\Sigma _\theta ) functional calculus for some θ ∈ ( 0 , π 2 ) \theta \in (0,\frac {\pi }{2}) can be dilated into a bounded analytic semigroup ( R t ) t ⩾ 0 (R_t)_{t\geqslant 0} on a bigger L p L^p -space in such a way that R t R_t is a positive contraction for any t ⩾ 0 t\geqslant 0 . We also establish a discrete analogue for Ritt operators and consider the case when L p L^p -spaces are replaced by more general Banach spaces. In connection with these functional calculus issues, we study isometric dilations of bounded continuous representations of amenable groups on Banach spaces and establish various generalizations of Dixmier’s unitarization theorem. |
| Databáze: | OpenAIRE |
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