Journal article
Certain ∗-homomorphisms of C∗-algebras and sequences of semicircular elements: A Banach space view
Illinois journal of mathematics, Vol.64(4), pp.519-567
12/01/2020
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 Xⱷ 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 Xⱷ. 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 Xⱷ. In particular, we outline how properties of those operators affect the semicircular law.
Details
- Title: Subtitle
- Certain ∗-homomorphisms of C∗-algebras and sequences of semicircular elements: A Banach space view
- Creators
- Ilwoo ChoPalle E. T. Jorgensen
- Resource Type
- Journal article
- Publication Details
- Illinois journal of mathematics, Vol.64(4), pp.519-567
- DOI
- 10.1215/00192082-8720474
- ISSN
- 0019-2082
- eISSN
- 1945-6581
- Language
- English
- Date published
- 12/01/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984240767702771
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