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A Joint Functional Calculus for Sectorial Operators with Commuting Resolvents
Author(s) -
Lancien F,
Lancien G,
Le Merdy C
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000501
Subject(s) - mathematics , hilbert space , banach space , linear subspace , pure mathematics , functional calculus , regular polygon , operator theory , holomorphic functional calculus , resolvent , bounded function , lattice (music) , finite rank operator , discrete mathematics , algebra over a field , calculus (dental) , mathematical analysis , medicine , physics , geometry , dentistry , acoustics
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.