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Definitizability of a Class of J ‐Selfadjoint Operators with Applications
Author(s) -
Behrndt Jussi,
Philipp Friedrich,
Trunk Carsten
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910302
Subject(s) - mathematics , hilbert space , operator (biology) , class (philosophy) , pure mathematics , perturbation (astronomy) , operator theory , computer science , physics , chemistry , quantum mechanics , biochemistry , repressor , artificial intelligence , transcription factor , gene
We formulate an abstract result concerning the definitizability of J ‐selfadjoint operators which, roughly speaking, differ by at most finitely many dimensions from the orthogonal sum of a J ‐selfadjoint operator with finitely many negative squares and a semibounded selfadjoint operator in a Hilbert space. The general perturbation result is applied to a class of singular Sturm–Liouville operators with indefinite weight functions. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)