Moore-Penrose inverse and partial orders on Hilbert space operators

GUILLERMINA FONGI; MARÍA CELESTE GONZALEZ

LINEAR ALGEBRA AND ITS APPLICATIONS

ELSEVIER SCIENCE INC

Año: 2023 vol. 674 p. 1 - 20

0024-3795

In this article we explore several aspects concerning to the Moore-Penrose inverse of a bounded linear operator. On the one hand, we study monotonicity properties of the Moore-Penrose inverse  with respect to the L"owner, star, minus, sharp and diamond orders. On the other hand, we analyze the validity of the reverse order law, $B^dagger A^dagger=(AB)^dagger$, under hypothesis of operator ranges and also under hypothesis of order operators. Finally, we study  the operator $B^dagger A^dagger$ as different weighted inverses of $AB$