Geodesic
Semicrossed Products of the Disk Algebra and the Jacobson Radical
Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 80-89

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DOI

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.
DOI : 10.4153/CMB-2012-018-8
Mots-clés : 47L65, 47L20, 30J10, 30H50, semicrossed product, disk algebra, Jacobson radical 
Khemphet, Anchalee; Peters, Justin R. Semicrossed Products of the Disk Algebra and the Jacobson Radical. Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 80-89. doi: 10.4153/CMB-2012-018-8
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     title = {Semicrossed {Products} of the {Disk} {Algebra} and the {Jacobson} {Radical}},
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