On the diagonal of Riesz operators on Banach lattices

Autor:	Drnovšek, Roman, Kandić, Marko
Rok vydání:	2022
Předmět:	Mathematics - Functional Analysis 46A40 46B42 47B06 47B07
Druh dokumentu:	Working Paper
Popis:	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 $\mathscr D$ of regular operators for which the diagonal coincides with the atomic diagonal is always a band in $\mathcal L_r(E)$, which contains the band of abstract integral operators. If $E$ is also a Banach lattice, then $\mathscr D$ contains positive Riesz operators. Comment: 16 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.10243 Zobrazit plný text záznamu View this record from Arxiv