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oai:docta.ucm.es:20.500.14352/725842025-01-20T16:51:15Zcom_20.500.14352_14col_20.500.14352_15

Operator ranges and endomorphisms with a prescribed behaviour on Banach spaces Jiménez Sevilla, María Del Mar Lajara, Sebastián 517.982.22 Separable Banach spaces Nuclear operators Operator ranges Invariant subspaces Chains of subspaces Análisis funcional y teoría de operadores We obtain several extensions of a theorem of Shevchik which asserts that if R is a proper dense operator range in a separable Banach space E, then there exists a compact, one-to-one and dense-range operator T : E → E such that T(E) ∩ R = {0}, and some results of Chalendar and Partington concerning the existence of compact, one-to-one and dense-range endomorphisms on a separable Banach space E which leave invariant a given closed subspace Y ⊂ E, or more generally, a countable increasing chain of closed subspaces of E. Ministerio de Ciencia e Innovación (MICINN) Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas Instituto de Matemática Interdisciplinar (IMI) FALSE unpub 2023-06-22T12:28:05Z 2023-06-22T12:28:05Z 2022-06 journal article https://hdl.handle.net/20.500.14352/72584 XXXX-XXXX eng PGC2018-097286-B-I00; MTM2017-86182-P open access application/pdf application/pdf