On convoluters on $L^p$-spaces

Abstract

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.

Author accepted version; to appear in Studia Math

References in corpus (2)

• Simple Lie groups without the Approximation Property II
• The $p$-approximation property for simple Lie groups with finite center

Cited by in corpus (4)

• Rigidity results for $L^p$-operator algebras and applications
• Multiplier algebras of $L^p$-operator algebras
• The approximation property for locally compact quantum groups
• A modern look at algebras of operators on $L^p$-spaces