The structures and decompositions of symmetries involving idempotents

Yuan Li, Jiaxin Zhang, Nana Wei

Let $\mathcal{H}$ be a separable Hilbert space and $P$ be an idempotent on $\mathcal{H}.$ We denote by $${\Gamma }_P=\{J:J=J^{\ast }=J^{-1}andJPJ=I-P\}$$ and $…