# SPECTRAL MAPPING THEOREMS FOR HOLOMORPHIC FUNCTIONAL CALCULI

@inproceedings{Haase2005SPECTRALMT, title={SPECTRAL MAPPING THEOREMS FOR HOLOMORPHIC FUNCTIONAL CALCULI}, author={Markus Haase}, year={2005} }

- Published 2005
DOI:10.1112/S0024610705006538

A spectral inclusion theorem and a spectral mapping theorem are proved for the functional calculus for sectorial operators. Most proofs are generic, so that similar results can be obtained for other functional calculi. Applications are a new proof for the spectral mapping theorem for fractional powers and the identity σ(log A) = log(σ(A) \ {0}) for any injective sectorial operator A.