English

Spectra of anticommutator for two orthogonal projections

Spectral Theory 2017-11-16 v2 Functional Analysis

Abstract

In this note, for any two orthogonal projection P,QP,Q on a Hilbert space, the characterization of spectrum of anticommutator PQ+QPPQ+QP has been obtained. As a corollary, the norm formula PQ+QP=PQ+PQ2\parallel PQ+QP\parallel=\parallel PQ\parallel+\parallel PQ\parallel^2 has been got an alternative proof (see Sam Waltrs, Anticommutator norm formula for projection operators, arXiv:1604.00699vl [math.FA] 3 Apr 2016)

Keywords

Cite

@article{arxiv.1705.05866,
  title  = {Spectra of anticommutator for two orthogonal projections},
  author = {Yan-Ni Dou and Hong-Ke Du and Yue-Qing Wang},
  journal= {arXiv preprint arXiv:1705.05866},
  year   = {2017}
}