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Dichotomy, bisectorial operators and unbounded spectral projections
Author(s) -
Winklmeier Monika,
Wyss Christian
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410481
Subject(s) - resolvent , bounded function , mathematics , operator (biology) , complex plane , unbounded operator , perturbation (astronomy) , bounded operator , resolvent formalism , mathematical analysis , pure mathematics , spectral theorem , plane (geometry) , finite rank operator , operator theory , physics , geometry , banach space , quantum mechanics , biochemistry , chemistry , repressor , transcription factor , gene
For an operator having a uniformly bounded resolvent on a strip around the imaginary axis, the existence of—possibly unbounded—spectral projections corresponding to the left and right half‐plane is proved. The operator is dichotomous if these projections are bounded, and an abstract perturbation theorem for dichotomy is derived. All results apply, with certain simplifications, to bisectorial operators. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)