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Pablos Romo, Fernando 2025-03-05T15:35:03Z 2025-03-05T15:35:03Z 2021 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 [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. application/pdf eng Springer Core-nilpotent decomposition Linear map Infinite linear system Drazin inverse Group inverse Reflexive generalized inverse 12 Matemáticas Core-Nilpotent Endomorphisms of Infinite-Dimensional Vector Spaces info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://doi.org/10.1007/s00009-021-01732-6 PGC2018-099599-B-I00 J416/463AC03 info:eu-repo/semantics/openAccess Mediterranean Journal of Mathematics 18 84 1 23