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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

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.

Authors

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

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