RT Journal Article
T1 Invariant subspaces for positive operators on Banach spaces with unconditional basis
A1 Gallardo Gutiérrez, Eva Antonia
A1 González Doña, Javier
A1 Tradacete Pérez, Pedro
AB 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.
PB American Mathematical Society
SN 0002-9939
YR 2022
FD 2022-06-16
LK https://hdl.handle.net/20.500.14352/71793
UL https://hdl.handle.net/20.500.14352/71793
LA eng
NO Gallardo 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.
NO Ministerio de Ciencia, Innovación y Universidades (España)/Fondo Europeo de Desarrollo Regional
NO Centro de Excelencia Severo Ochoa
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 27 abr 2025