Semicrossed Products of the Disk Algebra and the Jacobson Radical. Issue 1 (14th March 2014)

• Record Type: Journal Article
• Authors: Khemphet, Anchalee; Peters, Justin R.
• Is Part Of: Canadian mathematical bulletin =. Volume 57:Issue 1(2014)
• Page Start: 80
• Page End: 89
• Publication Date: 2014-03-14
• Subjects: 47L65 -- 47L20 -- 30J10 -- 30H50; semicrossed product -- disk algebra -- Jacobson radical; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2012-018-8
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: 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.