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SPECTRAL MAPPING THEOREMS FOR HOLOMORPHIC FUNCTIONAL CALCULI

Published online by Cambridge University Press:  24 May 2005

MARKUS HAASE
MARKUS HAASE
Affiliation:
Abteilung Angewandte Analysis, Universität Ulm, Helmholtzstrasse 18, 89069 Ulm, Germanyhaase@mathematik.uni-ulm.de
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Abstract

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 $\sigma(\log A)\,{=}\,\log(\sigma(A)\ohne\{0\})$ for any injective sectorial operator $A$.

Keywords

47A6047D06
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 723 - 739
Copyright
The London Mathematical Society 2005

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