an:01060881
Zbl 0904.47015
Lancien, Florence; Lancien, Gilles; Le Merdy, Christian
A joint functional calculus for sectorial operators with commuting resolvents
EN
Proc. Lond. Math. Soc., III. Ser. 77, No. 2, 387-414 (1998).
00050220
1998
j
47A60 47D06 46H30
joint functional calculus; resolvent commuting sectorial operators; \(B\)-convex Banach lattice; generalized \(H^\infty\) functional calculus; maximal regularity problem
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.
C.Le Merdy (Besancon)