The essential norm of multiplication operators on $$L_p(\mu )$$

Abstract

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