arXiv subjects

María Celeste Gonzalez

Publications and source records attributed to María Celeste Gonzalez.

3 recordsLinked to original sources

arXiv2026

Proper splittings of Hermitian operators

In this article we deepen the study of proper splittings of Hilbert space operators, with special emphasis on proper splittings of Hermitian operators. On the one hand, we improve characterizations given in [Fongi $\&$ Gonzalez, J. Math. Anal. Appl., 545 (2025) 129093] of the convergence of both the polar proper and the Moore Penrose proper splittings. On the other hand, we introduce new proper splittings and we compare their convergence with those of the polar and the Moore Penrose proper splittings.

math.FA↗

arXiv2024

Proper splittings of Hilbert space operators

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear operators defined on Hilbert spaces. We study the convergence of general proper splittings of operators in the infinite dimensional context. We also propose some particular splittings for special classes of operators and we study different criteria of convergence and comparison for them. In some cases, these criteria are given under hypothesis of operator order relations. In addition, we relate these results with the concept of the symmetric approximation of a frame in a Hilbert space.

math.FA↗

arXiv2022

Moore-Penrose inverse and partial orders on Hilbert space operators

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 Löwner, 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 $AB$.

math.FA↗