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Semicrossed Products of the Disk Algebra and the Jacobson Radical

Published online by Cambridge University Press:  20 November 2018

Anchalee Khemphet  and
Justin R. Peters
Anchalee Khemphet
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa, USA e-mail: khemphet@iastate.edu
Justin R. Peters
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa, USA e-mail: peters@iastate.edu
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Abstract

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We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson radical of these operator algebras. Furthermore, in the case that the finite Blaschke product is elliptic, we show that the semicrossed product contains no nonzero quasinilpotent elements. However, if the finite Blaschke product is hyperbolic or parabolic with positive hyperbolic step, the Jacobson radical is nonzero and a proper subset of the set of quasinilpotent elements.

Keywords

47L6547L2030J1030H50semicrossed productdisk algebraJacobson radical
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 80 - 89
Copyright
Copyright © Canadian Mathematical Society 2014

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