Jiménez Sevilla, María Del MarLajara, Sebastián2023-06-222023-06-222022-06https://hdl.handle.net/20.500.14352/72584We 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.engjournal articleopen access517.982.22Separable Banach spacesNuclear operatorsOperator rangesInvariant subspacesChains of subspacesAnálisis funcional y teoría de operadores