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.
- Received: 2017-06-12.
- Accepted: 2017-08-21.
- Published online: 2018-04-11.
