The essential spectrum, norm, and spectral radius of abstract multiplication operators

Anton R. Schep

Let $E$ be a complex Banach lattice and $T$ is an operator in the centrum $Z(E)=\{T: |T|\le λI \mbox{ for some } λ\}$ of $E$. Then the essential norm $\Vert T{\Vert }_e$ of $T$ equals the…