This is an announcement for the paper “Multiplication operators on $L^p$” by March Boedihardjohttps://arxiv.org/find/math/1/au:+Boedihardjo_M/0/1/0/all/0/1.

Abstract: We show that every operator on $L_p, 1<p<\infty$ defined by multiplication by the identity function on $\mathbb{C}$ is a compact perturbation of an operator that is diagonal with respect to an unconditional basis. We also classify these operators up to similarity modulo compact operators and up to approximate similarity.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1707.04798