Identities concerning the reverse order law for the Moore–Penrose inverse

摘要

We prove some identities related to the reverse order law for the Moore–Penrose inverse of operators on Hilbert spaces, extending some results from (Y. Tian, S. Cheng, Linear Multilinear Algebra 52 (2004)) and (R. E. Cline, SIAM Rev., Vol. 6, No. 1 (1964)) to infinite dimensional settings.