Multiplication operators on $L^{p}$
Volume 244 / 2019
Studia Mathematica 244 (2019), 309-319
MSC: Primary 47B38.
DOI: 10.4064/sm170903-15-11
Published online: 21 May 2018
Abstract
We show that every operator on $L^{p}$, $1 \lt p \lt \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.
