Author:
Albrecht David,Franks Edwin,McIntosh Alan
Abstract
Let S and T be commuting operators of type ω and type ϖ in a Banach space X. Then the pair has a joint holomorphic functional calculus in the sense that it is possible to define operators f(S, T) in a consistent manner, when f is a suitable holomorphic function defined on a product of sectors. In particular, this gives a way to define the sum S + T when ω + ϖ < π. We show that this operator is always of type μ where μ = max{ω, ϖ}. We explore when bounds on the individual functional calculi of S and T imply bounds on the functional calculus of the pair (S, T), and some implications for the regularity problem of when ∥(S + T)u∥ is equivalent to ∥Su∥ + ∥Tu∥.
Publisher
Cambridge University Press (CUP)
Cited by
12 articles.
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