Spaces of Bounded Measurable Functions Invariant Under a Group Action

Abstract

In this paper we characterize spaces of $L^{\infty }$-functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work generalizes the author's 2021 results concerning the specific case of unitarily and Möbius invariant spaces of $L^{\infty }$-functions defined on the unit sphere in ${\mathbb{C}}^n$.

arXiv commentarXiv admin note: text overlap with arXiv:2110.12060