On the diagonal of Riesz operators on Banach lattices

This paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz operator on an order continuous Banach lattice yields that the spectrum of such operator lies on its diagonal, which motiva...

Full description

Saved in:
Bibliographic Details
Published in:Quaestiones mathematicae 2024-03, Vol.47 (sup1), p.137-151
Main Authors: Drnovšek, R., Kandić, M.
Format: Article
Language:English
Subjects:
Banach lattices
Banach spaces
diagonal of an operator
Lattices (mathematics)
Linear operators
Operators (mathematics)
Riesz operators
Vector lattices
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz operator on an order continuous Banach lattice yields that the spectrum of such operator lies on its diagonal, which motivates the systematic study of an abstract diagonal of a regular operator on an order complete vector lattice E. We prove that the class of regular operators for which the diagonal coincides with the atomic diagonal is always a band in , which contains the band of abstract integral operators. If E is also a Banach lattice, then contains positive Riesz and positive AM-compact operators.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2023.2287829