No title - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Transactions of the American Mathematical Society Année : 2017

Résumé

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.

Dates et versions

hal-03525907 , version 1 (14-01-2022)

Identifiants

Citer

Cédric Arhancet, Stephan Fackler, Christian Le Merdy. No title. Transactions of the American Mathematical Society, 2017, 369 (10), pp.6899-6933. ⟨10.1090/tran/6849⟩. ⟨hal-03525907⟩
13 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More