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Spectral functions of products of selfadjoint operators
Author(s) -
Ya. Azizov T.,
Denisov M.,
Philipp F.
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200169
Subject(s) - mathematics , resolvent , gravitational singularity , operator (biology) , spectrum (functional analysis) , polynomial , function (biology) , pure mathematics , spectral theorem , spectral properties , operator theory , mathematical analysis , quantum mechanics , physics , biochemistry , chemistry , repressor , evolutionary biology , biology , astrophysics , transcription factor , gene
Given two possibly unbounded selfadjoint operators A and G such that the resolvent sets of AG and GA are non‐empty, it is shown that the operator AG has a spectral function on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb R$\end{document} with singularities if there exists a polynomial p ≠ 0 such that the symmetric operator Gp ( AG ) is non‐negative. This result generalizes a well‐known theorem for definitizable operators in Krein spaces.