Invariant subspaces for positive operators on Banach spaces with unconditional basis

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Gallardo Gutiérrez, Eva A. and González Doña, Javier and Tradacete Pérez, Pedro (2022) Invariant subspaces for positive operators on Banach spaces with unconditional basis. Proceedings of the American Mathematical Society . ISSN 0002-9939

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Official URL: https://doi.org/10.1090/proc%2F16026




Abstract

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.


Item Type:Article
Uncontrolled Keywords:Banach lattices; Lattice homomorphisms; Invariant subspaces; Invariant ideals
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:73564
Deposited On:12 Jul 2022 15:29
Last Modified:02 Aug 2022 08:44

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