Gallardo Gutiérrez, Eva AntoniaGonzález Doña, JavierTradacete Pérez, Pedro2023-06-222023-06-222022-06-16Gallardo Gutiérrez, E. A., González Doña, J. & Tradecete Pérez, P. Invariant subspaces for positive operators on Banach spaces with unconditional basis. 16 de febrero de 2022. Proceedings of the American Mathematical Society, https://doi.org/10.1090/proc/16026.0002-993910.1090/proc/16026https://hdl.handle.net/20.500.14352/71793We 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.engjournal articlehttps://doi.org/10.1090/proc%2F16026https://www.ams.org/journals/proc/0000-000-00/S0002-9939-2022-16026-2/open access517.982.22Banach latticesLattice homomorphismsInvariant subspacesInvariant idealsAnálisis funcional y teoría de operadores