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Semicrossed Products of the Disk Algebra and the Jacobson Radical

  Published:2012-08-25
 Printed: Mar 2014
  • Anchalee Khemphet,
    Department of Mathematics, Iowa State University, Ames, Iowa, USA
  • Justin R. Peters,
    Department of Mathematics, Iowa State University, Ames, Iowa, USA
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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 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: semicrossed product, disk algebra, Jacobson radical semicrossed product, disk algebra, Jacobson radical
MSC Classifications: 47L65, 47L20, 30J10, 30H50 show english descriptions Crossed product algebras (analytic crossed products)
Operator ideals [See also 47B10]
Blaschke products
Algebras of analytic functions
47L65 - Crossed product algebras (analytic crossed products)
47L20 - Operator ideals [See also 47B10]
30J10 - Blaschke products
30H50 - Algebras of analytic functions
 

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