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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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