Invariant subspaces and group invertibility of closed linear relations
Date
2026-02-24
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Benemérita Universidad Autónoma de Puebla
Abstract
“The concept of linear relation was introduced by J. von Neumann [10] due to the need to consider differential operators that are not densely defined. Subsequently, M. Gromov studied differential operators, giving rise to the need to further develop the notions introduced by Neumann. Likewise, A. Favini and A. Yagi ([6]) drew upon these new theoretical results to apply methods involving the construction of linear relations in order to solve differential equations. This notion has been extensively studied in the literature due to its usefulness in several areas, including the theory of differential equations ([1], [2], [6]), degenerate semigroups of operators [3, 4] and analysis of generalized inverses ([7], [8], [9]). Interest in the theory of linear relations has increased in recent years, a several important and recent results can be find in [1], [7], [8] and [9]. We like to put out the Baskakov’s important work presented in [4], the articles that largely inspire some of our postulates. The notations and definitions of some concepts may be different from ones used in the reference literature, however, mainly those are inspired by [4] and [5]. Beyond our great mathematical interest in the area, the main motivation for this work is that linear relations have the potential to be applied in many fields, such is the case of Inverse Problems and Regularization Theory”.
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