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arXiv · 2005.01150

Invariant subspaces for positive operators on Banach spaces with unconditional basis

Eva A. Gallardo-Gutiérrez·Javier González-Doña·Pedro Tradacete
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Abstract

We prove that every lattice homomorphism acting on a Banach space $\mathcal{X}$ 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 later examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on $\mathcal{X}$ extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.

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Eva A. Gallardo-Gutiérrez, Javier González-Doña, Pedro Tradacete. 2020-05-03. Invariant subspaces for positive operators on Banach spaces with unconditional basis. https://arxiv.org/abs/2005.01150

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