SEMICROSSED PRODUCTS OF THE DISK ALGEBRA.

If α is the endomorphism of the disk algebra, A(D), induced by composition with a finite Blaschke product b, then the semicrossed product A(D) ×α Z+ imbeds canonically, completely isometrically into C(T) ×α Z+. Hence in the case of a non-constant Blaschke product b, the C*-envelope has the form C(Sb) ×s Z, where (Sb, s) is the solenoid system for (T, b). In the case where b is a constant, the C*-envelope of A(D) ×α Z+ is strongly Morita equivalent to a crossed product of the form C0(Se) ×s Z, where e: T × N -→ T × N is a suitable map and (Se, s) is the solenoid system for (T × N, e). [ABSTRACT FROM AUTHOR]