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Multiplication operators on $L^{p}$

Volume 244 / 2019

March T. Boedihardjo Studia Mathematica 244 (2019), 309-319 MSC: Primary 47B38. DOI: 10.4064/sm170903-15-11 Published online: 21 May 2018


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.


  • March T. BoedihardjoDepartment of Mathematics
    University of California
    Los Angeles, CA 90095-1555, U.S.A.

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