Spectral functions of products of selfadjoint operators

Details Spectral functions of products of selfadjoint operators Spectral functions of products of selfadjoint operators

2011-07-08

arxiv.org/abs/1107.1618v2

Mathematics

Spectral Theory

Scientific paper

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.

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