𝐻^{∞}-calculus for the sum of non-commuting operators

Prüss, Jan; Simonett, Gieri

doi:10.1090/S0002-9947-07-04291-2

$H^\infty$-calculus for the sum of non-commuting operators
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Trans. Amer. Math. Soc. 359 (2007), 3549-3565 Request permission

Abstract:

A recent result of Kalton and Weis is extended to the case of non-commuting operators, employing the commutator condition of Labbas and Terreni, or of Da Prato and Grisvard. Under appropriate assumptions it is shown that the sum of two non-commuting operators admits an $\mathcal H^\infty$-calculus. The main results are then applied to a parabolic problem on a wedge domain.

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