%0 Journal Article
%A Gallardo Gutiérrez, Eva A.
%A González Doña, Javier
%A Tradacete Pérez, Pedro
%T Invariant subspaces for positive operators on Banach spaces with unconditional basis
%D 2022
%@ 0002-9939
%U https://hdl.handle.net/20.500.14352/71793
%X We prove that every lattice homomorphism acting on a Banach space X with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on X extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.
%~