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Spectral Mapping Theorems for Holomorphic Functional Calculi
Author(s) -
Haase Markus
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006538
Subject(s) - injective function , mathematical proof , mathematics , functional calculus , pure mathematics , operator (biology) , spectral theorem , holomorphic function , discrete mathematics , operator theory , calculus (dental) , geometry , medicine , biochemistry , chemistry , dentistry , repressor , transcription factor , gene
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 .
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