RT Journal Article
T1 Band-diagonal operators on Banach lattices: matrix dynamics and invariant subspaces
A1 Gallardo Gutiérrez, Eva Antonia
A1 González Doña, Javier
AB We address the existence of non-trivial closed invariant ideals for positive operators defined on Banach lattices whose order is induced by an unconditional basis. In particular, for band-diagonal positive operators such existence is characterized whenever their matrix representations meet a positiveness criteria. For more general classes of positive operators, sufficient conditions are derived proving, particularly, the sharpness of such results from the standpoint of view of the matrix representations. The whole approach is based on studying the behavior of the dynamics of infinite matrices and the localization of the non-zero entries. Finally, we generalize a theorem of Grivaux regarding the existence of non-trivial closed invariant subspaces for positive tridiagonal operators to a more general class of band-diagonal operators showing, in particular, that a large subclass of them have non-trivial closed invariant subspaces but lack non-trivial closed invariant ideals.
PB Elsevier Science
SN 0024-3795
YR 2023
FD 2023
LK https://hdl.handle.net/20.500.14352/72424
UL https://hdl.handle.net/20.500.14352/72424
LA eng
NO Ministerio de Ciencia e Innovación
DS Docta Complutense
RD 4 abr 2025