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A jointfunctional calculus for sectorial operators with commuting resolvents

Published online by Cambridge University Press:  01 September 1998

G Lancien
Affiliation:
C Le Merdy
Affiliation:
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Abstract

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 $H^\infty$-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.

1991 Mathematics Subject Classification: 47A60, 47D06, 46C15.

Type
Research Article
Copyright
London Mathematical Society 1998

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