caa a22 4500 467931976 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20061001xx s 000 0 eng 10.1007/s00020-006-1418-4 doi (NATIONALLICENCE)springer-10.1007/s00020-006-1418-4 Haase Markus Department of Pure Mathematics, University of Leeds, LS12 3RQ, Leeds, United Kingdom aut Operator-valued H ∞-calculus in Inter- and Extrapolation Spaces [Elektronische Daten] [Markus Haase] Abstract.: We generalize a Hilbert space result by Auscher, McIntosh and Nahmod to arbitrary Banach spaces X and to not densely defined injective sectorial operators A. A convenient tool proves to be a certain universal extrapolation space associated with A. We characterize the real interpolation space $${\left( {X,\mathcal{D}{\left( {A^{\alpha } } \right)} \cap \mathcal{R}{\left( {A^{\alpha } } \right)}} \right)}_{{\theta ,p}} $$ as $$ {\left\{ {x\, \in \,X|t^{{ - \theta {\text{Re}}\alpha }} \psi _{1} {\left( {tA} \right)}x,\,t^{{ - \theta {\text{Re}}\alpha }} \psi _{2} {\left( {tA} \right)}x \in L_{*}^{p} {\left( {{\left( {0,\infty } \right)};X} \right)}} \right\}} $$ for a wide range of holomorphic functions ψ1, ψ2 and show that in this space the operator A has a bounded operator-valued H∞-functional calculus which is even R-bounded in case p < ∞. This generalizes results of Dore, Clément and Prüss. Consequences are a Da Prato-Grisvard theorem for injective commuting sectorial operators A, B and an adjoint-free proof of McIntosh's theorem. Finally, we investigate the functional calculus properties for non-invertible operators A on the spaces $${\left( {X,\mathcal{D}{\left( {A^{\alpha } } \right)}} \right)}_{{\theta ,p}} $$ . Birkhäuser Verlag, Basel, 2006 Functional calculus nationallicence interpolation space nationallicence extrapolation space nationallicence sectorial operator nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhäuser.ch 56/2(2006-10-01), 197-228 0378-620X 56:2<197 2006 56 20 https://doi.org/10.1007/s00020-006-1418-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-006-1418-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Haase Markus Department of Pure Mathematics, University of Leeds, LS12 3RQ, Leeds, United Kingdom aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhäuser.ch 56/2(2006-10-01), 197-228 0378-620X 56:2<197 2006 56 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer