Bombal Gordón, FernandoHernando Boto, Beatriz2023-06-202023-06-2019950373-8299https://hdl.handle.net/20.500.14352/58307Operators from a Banach space X into a Banach space Y weaker than isomorphisms and, nevertheless, preserving some isomorphic property, i.e. such that a good property of Y lifts to X, have been studied by many authors. This note is also devoted to that study; more precisely, given a complete σ-finite measure space (Ω,Σ,μ) into L1(μ) and given necessary and sufficient conditions for such an operator to be a Tauberian or semi-Tauberian operator, a semi-embedding or a ∗∗-injection, in the case when X is an Orlicz space, it is also proved that these conditions are equivalent to the reflexivity of X. The results obtained are applied to deduce properties of the vector-valued Köthe function space X(E), E a Banach space, from the corresponding properties of L1(μ,E).journal articlehttp://www.staff.amu.edu.pl/~commath/index.php?target=home&lang=enmetadata only access517.982.2Köthe functionGeometría diferencialAnálisis funcional y teoría de operadores1204.04 Geometría Diferencial