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oai:gredos.usal.es:10366/1640642026-01-20T11:08:19Zcom_10366_4540com_10366_4512com_10366_3823com_10366_4146com_10366_4055com_10366_3946col_10366_4541col_10366_4147

00925njm 22002777a 4500 dc Pablos Romo, Fernando author 2021 [EN]The aim of this work is to develop a general theory of core-nilpotent endomorphisms of arbitrary vector spaces, such that endomorphisms of finite-dimensional vector spaces and finite potent endomorphisms of infinite-dimensional vector spaces are particular cases of the CN-endomorphisms studied in this theory. For these CN-endomorphisms, we introduce an index that generalizes the index of a finite square matrix and we prove the existence of the Drazin inverse and reflexive generalized inverses. In particular, we characterize all endomorphisms that have Drazin inverse on arbitrary vector spaces. Moreover, we offer a method to study infinite linear systems associated with CN-endomorphisms. Pablos Romo, F. Core-Nilpotent Endomorphisms of Infinite-Dimensional Vector Spaces. Mediterr. J. Math. 18, 84 (2021). https://doi.org/10.1007/s00009-021-01732-6 1660-5446. 1660-5454 http://hdl.handle.net/10366/164064 10.1007/s00009-021-01732-6 Core-nilpotent decomposition Linear map Infinite linear system Drazin inverse Group inverse Reflexive generalized inverse Core-Nilpotent Endomorphisms of Infinite-Dimensional Vector Spaces