Proceedings of the London Mathematical Society · 1998 · 60 citations · 11 references
Natural SciencesMathematicsAlgebraRepresentation TheorySet TheoryFunctional MathematicsOperator TheoryBounded OperatorsFunctional Calculus For OperatorsOperator AlgebrasOperatorsResolvent OperatorsResolvent TheorySectorial OperatorsSubject Classification
In this paper we study the notion of joint functional calculus associated with a couple of resolvent commuting sectorial operators on 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 a generalized H∞-functional calculus associated with the extension to Λ(H) of a sectorial operator on a B-convex Banach lattice Λ, where H is a Hilbert space. We apply our results to a new construction of operators with a bounded H∞-functional calculus and to the maximal regularity problem. 1991 Mathematics Subject Classification: 47A60, 47D06, 46C15.
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