The essential norm of multiplication operators on Lp(μ)L_p(μ)

preprint2022arXivOpen access

Abstract

We show that the formula for the essential norm of a multiplication operator on LpL_p, for 1<p<∞1<p<\infty, also holds for p=1p=1. We also provide a proof for the formula which works simultaneously for all p∈[1,∞)p\in[1,\infty).

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