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6
votes
Accepted
Unbounded version of continuous functional calculus
You find the precise abstract statment in the Internet Seminar lecture notes of Markus Haase, especially in Chapter 4.
See
https://www.math.uni-kiel.de/isem21/en/course/phase1
By the way, the answer …
1
vote
The derivative of a $C_0$-semigroup with respect to a perturbation parameter
I think Theorem 2.20 in Chapter IX of Kato,
Kato, Tosio, Perturbation theory for linear operators., Classics in Mathematics. Berlin: Springer-Verlag. xxi, 619 p. (1995). ZBL0836.47009.
has something t …