Quasinilpotent Linear Relations : Insights, structure and applications

Puntos clave

Quasinilpotent linear relations can be reclassified as nilpotent under specific conditions, indicating a nuanced understanding of their structure.
The study introduces R-quasinilpotent relations, expanding current concepts related to linear relations in functional analysis.
Analysis focuses on ascent, descent, and closure of iterated images within the context of Banach spaces.
The implications of generalized Drazin invertible relations point to future applications in mathematical theory and practice.

Resumen

This paper explores the concepts of nilpotent and quasinilpotent linear relations in the context of Banach spaces. We establish sufficient conditions under which a quasinilpotent linear relation can be classified as nilpotent, focusing on the finiteness of ascent and descent and the closure of iterated images. We then introduce and analyze the class of meromorphic linear relations, emphasizing conditions that lead to their classification as quasinilpotent. Furthermore, we expand on the notion of quasinilpotent linear relations by introducing the concept of regularity and defining R-quasinilpotent relations. As an application, we investigate generalized Drazin invertible relations related to a given regularity.

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Cite This Study

Benchabane et al. (Fri,) studied this question.

synapsesocial.com/papers/690e8b6ca5b062d7a4e73513 https://doi.org/https://doi.org/10.1142/s0219498827500915

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