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December 2020 Certain -homomorphisms of C-algebras and sequences of semicircular elements: A Banach space view
Ilwoo Cho, Palle E. T. Jorgensen
Illinois J. Math. 64(4): 519-567 (December 2020). DOI: 10.1215/00192082-8720474

Abstract

In this paper, we study deformation in free probability theory. Our setting is systems of specific Banach-space operators acting on a C-algebra Xφ generated by mutually free, infinitely-many semicircular elements. In particular, we give a constructive classification for the cases where those operators are generated by certain -homomorphisms on Xφ. Our main results not only classify and characterize specific types of the operators, but they also show how such operators deform the free probability on Xφ. In particular, we outline how properties of those operators affect the semicircular law.

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Ilwoo Cho. Palle E. T. Jorgensen. "Certain -homomorphisms of C-algebras and sequences of semicircular elements: A Banach space view." Illinois J. Math. 64 (4) 519 - 567, December 2020. https://doi.org/10.1215/00192082-8720474

Information

Received: 25 September 2019; Revised: 25 May 2020; Published: December 2020
First available in Project Euclid: 28 September 2020

zbMATH: 07269219
MathSciNet: MR4164445
Digital Object Identifier: 10.1215/00192082-8720474

Subjects:
Primary: 46L10
Secondary: 46L54, 47L55

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 4 • December 2020
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