Certain invariant spaces of bounded measurable functions on a sphere

Abstract

In their 1976 paper, Nagel and Rudin characterize the closed unitarily and Möbius invariant spaces of continuous and \(L^p\)-functions on a sphere, for \(1\le p<\infty \). In this paper we provide an analogous characterization for the weak*-closed unitarily and Möbius invariant spaces of \(L^\infty \)-functions on a sphere. We also investigate the weak*-closed unitarily and Möbius invariant algebras of \(L^\infty \)-functions on a sphere.