Some norm inequalities concerning generalized inverses
The von Neumann-Schatten class \({\mathcal C}_ p\) consists of the compact linear operators \(A\) on a Hilbert space such that the eigenvalues of \((A^*A)^{1/2}\) are in \(\ell^ p\). This paper extends \textit{R. Penrose}'s result on the minimization of \(\| AX-B\|_ 2\) to the \(\|\cdot\|_ p\) norm on \({\mathcal C}_ p\) [Proc. Camb. Philos. Soc. 52, 17-19 (1956; Zbl 0070.125)]. Related minimization problems are also considered.
scientific article; zbMATH DE number 69523