Semicrossed Products of the Disk Algebra and the Jacobson Radical

Canadian mathematical bulletin

Anchalee Khemphet¹  Justin R. Peters¹ 

[1] Department of Mathematics, Iowa State University, Ames, Iowa, USA

关键词: semicrossed product;    disk algebra;    Jacobson radical;   

DOI  :  10.4153/CMB-2012-018-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We consider semicrossed products of the disk algebra with respect toendomorphisms defined by finite Blaschke products. We characterize the Jacobson radicalof these operator algebras. Furthermore, in the case the finite Blaschke product is elliptic, we show that the semicrossed product contains no nonzero quasinilpotentelements. 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.

【 授权许可】

Unknown