Spectral functions of products of selfadjoint operators
Spectral Theory
2011-07-12 v2
Abstract
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 IR with singularities if there exists a non-zero polynomial p such that the symmetric operator Gp(AG) is non-negative. This result generalizes a well-known theorem for definitizable operators in Krein spaces.
Keywords
Cite
@article{arxiv.1107.1618,
title = {Spectral functions of products of selfadjoint operators},
author = {Tomas Ya. Azizov and Mikhail Denisov and Friedrich Philipp},
journal= {arXiv preprint arXiv:1107.1618},
year = {2011}
}