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A joint functional calculus for sectorial operators with commuting resolvents. (English) Zbl 0904.47015
We study the notion of joint functional calculus associated with a couple of resolvent commuting sectorial operators in a Banach space $$X$$. We present some positive results when $$X$$ is for example a Banach lattice or a quotient of subspaces of a $$B$$-convex Banach lattice. Furthermore, we develop a notion of generalized $$H^\infty$$ functional calculus associated with the extension to $$\Lambda(H)$$ of a sectorial operator on a $$B$$-convex Banach lattice $$\Lambda$$, where $$H$$ is a Hilbert space. We apply our results to a new construction of operators with a bounded $$H^\infty$$ functional calculus and to the maximal regularity problem.

##### MSC:
 47A60 Functional calculus for linear operators 47D06 One-parameter semigroups and linear evolution equations 46H30 Functional calculus in topological algebras
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