Spectra of anticommutator for two orthogonal projections
Yan-Ni Dou, Yueqing Wang, Miaomiao Cui, Hong-Ke Du · Linear and Multilinear Algebra · 2018
In this note, for any two orthogonal projections P,Q on a Hilbert space, the characterization of spectrum of anticommutator PQ+QP has been obtained. As a corollary, an alternative proof of the norm formula ∥PQ+QP∥=∥PQ∥+∥PQ∥2 has been obtained (see Walters S. Anticommutator norm formula for projection operators, arXiv:1604.00699vl [math.FA] 3 Apr 2016).