On convoluters on $L^p$-spaces
Volume 245 / 2019
Studia Mathematica 245 (2019), 15-31 MSC: Primary 43A15; Secondary 22D12, 47L10. DOI: 10.4064/sm170601-24-11 Published online: 29 June 2018
We prove two theorems about convolution operators on $L^p(G)$ for a locally compact group $G$. First, if $G$ has the approximation property, then the algebra of convoluters is the algebra of pseudo-measures. Second, the bicommutant of the algebra of pseudo-measures is the algebra of convoluters.