Semicrossed products of the disc algebra

2011/04/07 by Kenneth R. Davidson, Davidson, Kenneth R., Elias G. Katsoulis +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1104.1398

7 pages

arxiv created 2011/04/07 · openalex publication_date 2011/04/07 · arxiv updated 2011/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If α is the endomorphism of the disk algebra, \AD, induced by composition with a finite Blaschke product b, then the semicrossed product \AD×_α \bZ⁺ imbeds canonically, completely isometrically into \rC(\bT)×_α \bZ⁺. Hence in the case of a non-constant Blaschke product b, the C*-envelope has the form \rC(§_b)×_s \bZ, where (§_b, s) is the solenoid system for (\bT, b). In the case where b is a constant, then the C*-envelope of \AD×_α \bZ⁺ is strongly Morita equivalent to a crossed product of the form \rC(§_e)×_s \bZ, where e \colon \bT × \bN \longrightarrow \bT × \bN is a suitable map and (§_e, s) is the solenoid system for (\bT × \bN, e) .

Citations

• Adding tails to C*-correspondences

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