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Spectral points of definite type and type π for linear operators and relations in Krein spaces
Author(s) -
Azizov T. Ya.,
Behrndt J.,
Jonas P.,
Trunk C.
Publication year - 2011
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/jlms/jdq098
Subject(s) - mathematics , type (biology) , bounded function , mathematical analysis , perturbation (astronomy) , sign (mathematics) , spectral theorem , operator theory , linear operators , pure mathematics , spectral properties , hilbert space , physics , quantum mechanics , ecology , astrophysics , biology
Spectral points of positive and negative type, and type π + and type π − for closed linear operators and relations in Krein spaces are introduced with the help of approximative eigensequences. The main objective of the paper is to study these sign type properties in the non‐self‐adjoint case under various kinds of perturbations, for example, compact perturbations and perturbations small in the gap metric. Many of the obtained perturbation results are also new for the special case of bounded and unbounded self‐adjoint operators in Krein spaces.