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arXiv · 2211.05037

Moore-Penrose inverse and partial orders on Hilbert space operators

Guillermina Fongi·María Celeste Gonzalez
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Abstract

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 $AB$.

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Guillermina Fongi, María Celeste Gonzalez. 2022-11-09. Moore-Penrose inverse and partial orders on Hilbert space operators. https://arxiv.org/abs/2211.05037

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