On the diagonal of Riesz operators on Banach latticesDrnovšek, Roman (Avtor) Kandić, Marko (Avtor) vector latticesBanach latticesRiesz operatorsdiagonal of an operatorThis 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 and positive AM-compact operators.20242024-03-21 12:58:23Članek v reviji155239UDK: 517.9ISSN pri članku: 1607-3606DOI: 10.2989/16073606.2023.2287829COBISS_ID: 188345347sl