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 ≤ p < ∞. In this paper we provide an analogous characterization for the weak*-closed unitarily and Möbius invariant spaces of L ∞ -functions on a sphere. We also investigate the weak*-closed unitarily and Möbius invariant algebras of L ∞ -functions on a sphere.