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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

Core-Nilpotent Endomorphisms of Infinite-Dimensional Vector Spaces Pablos Romo, Fernando Core-nilpotent decomposition Linear map Infinite linear system Drazin inverse Group inverse Reflexive generalized inverse [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. 2025-03-05T15:35:03Z 2025-03-05T15:35:03Z 2025-03-05T15:35:03Z 2021 info:eu-repo/semantics/article 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 eng https://doi.org/10.1007/s00009-021-01732-6 PGC2018-099599-B-I00 J416/463AC03 info:eu-repo/semantics/openAccess Springer