Von Neumann algebras of analytic functions on the unit ball

Abstract

This paper is an attempt to answer the challenge posed by Ma and Zhu in [3]. We provide examples of von Neumann algebras of holomorphic functions over the unit disc as well as over the unit ball. In the end, we introduce a novel multiplication operation on the set of all holomorphic functions over the unit disc, ensuring that this collection forms a ⁎-algebra of analytic functions over D.