论文标题
在Riesz Operators的对角线上
On the diagonal of Riesz operators on Banach lattices
论文作者
论文摘要
本文将紧凑型操作员的众所周知的环形理论扩展到Banach空间上的多项式Riesz操作员。理想三角形的Riesz操作员在连续的Banach晶格上的特殊情况表明，该操作员的光谱在于其对角线，这激发了对常规操作员在订单完整矢量vector lattice $ e $ e $上的较对角线的系统研究。我们证明，与原子对角线重合对角线的常规操作员的类$ \ Mathscr d $始终是$ \ Mathcal l_r（E）$的频段，其中包含抽象积分运算符的频段。如果$ e $也是Banach晶格，则$ \ Mathscr d $包含正Riesz运营商。
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.
