Opuscula Math. 38, no. 4 (2018), 501-535

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.
Opuscula Mathematica - cover

Cite this article as:
Ilwoo Cho, Palle E. T. Jorgensen, Banach *-algebras generated by semicircular elements induced by certain orthogonal projections, Opuscula Math. 38, no. 4 (2018), 501-535, https://doi.org/10.7494/OpMath.2018.38.4.501

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