Opuscula Math. 38, no. 4 (2018), 501-535
https://doi.org/10.7494/OpMath.2018.38.4.501

Opuscula Mathematica

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

Ilwoo Cho
Palle E. T. Jorgensen

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.

Mathematics Subject Classification: 46L10, 46L54, 47L15, 47L30, 47L55.

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• Ilwoo Cho
• Saint Ambrose University, Department of Mathematics and Statistics, 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803, USA
• Palle E. T. Jorgensen
• The University of Iowa, Department of Mathematics, Iowa City, IA 52242-1419, USA
• Communicated by P.A. Cojuhari.
• Accepted: 2017-08-21.
• Published online: 2018-04-11.