Banach *-algebras generated by semicircular elements induced by certain orthogonal projections

Abstract

The main purpose of this paper is to study structure theorems of Banach \(*\)-algebras generated by semicircular elements. In particular, we are interested in the cases where given semicircular elements are induced by orthogonal projections in a \(C^{*}\)-probability space.

Keywords

• free probability
• orthogonal projections
• weighted-semicircular elements
• semicircular elements