On Davis-Kahan-Weinberger extension theorem

Abstract

If $R=\text{bmatrix}HB\text{endbmatrix}$, where $H=H^{\ast }$, we find a pseudo-inverse form of all solutions $W=W^{\ast }$, such that $\Vert A\Vert =\Vert R\Vert$, where and $\Vert H\Vert \le \Vert R\Vert$. In this paper we extend well-known results in a finite dimensional setting, proved by Dao-Sheng Zheng [15]. Thus, a pseudo inverse form of solutions of the Davis-Kahan-Weinberger theorem is established.