Semicrossed products of the disk algebra

Authors:
Kenneth R. Davidson and Elias G. Katsoulis

Journal:
Proc. Amer. Math. Soc. **140** (2012), 3479-3484

MSC (2000):
Primary 47L55

DOI:
https://doi.org/10.1090/S0002-9939-2012-11348-6

Published electronically:
February 17, 2012

MathSciNet review:
2929016

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If is the endomorphism of the disk algebra, , induced by composition with a finite Blaschke product , then the semicrossed product imbeds canonically, completely isometrically into . Hence in the case of a non-constant Blaschke product , the C*-envelope has the form , where is the solenoid system for . In the case where is a constant, the C*-envelope of is strongly Morita equivalent to a crossed product of the form , where is a suitable map and is the solenoid system for .

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Additional Information

**Kenneth R. Davidson**

Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L–3G1, Canada

Email:
krdavids@uwaterloo.ca

**Elias G. Katsoulis**

Affiliation:
Department of Mathematics, University of Athens, 15784 Athens, Greece

Address at time of publication:
Department of Mathematics, East Carolina University, Greenville, North Carolina 27858.

Email:
katsoulise@ecu.edu

DOI:
https://doi.org/10.1090/S0002-9939-2012-11348-6

Keywords:
Semicrossed product,
crossed product,
disk algebra,
C*-envelope

Received by editor(s):
April 7, 2011

Published electronically:
February 17, 2012

Additional Notes:
The first author was partially supported by an NSERC grant.

The second author was partially supported by a grant from the ECU

Communicated by:
Marius Junge

Article copyright:
© Copyright 2012
American Mathematical Society