The C~*-algebra generated by the strong Θ-operator is considered in this paper. Thepaper contains two parts. The first part shows that the commutant ideal I(T) of C(T) is*isomorphic to where ?_n ??_(n+1), n = 1,2,…a...The C~*-algebra generated by the strong Θ-operator is considered in this paper. Thepaper contains two parts. The first part shows that the commutant ideal I(T) of C(T) is*isomorphic to where ?_n ??_(n+1), n = 1,2,…and ?_n is * isomorphic to the n-matrix algebra over C_0(Z_0). In particular, when T is a completely nonnormal strong Θ-operator, I(T) is * isomorphic to C_0(Z_0)(×)K(I^2). The second part gives the equivalent con-ditions which make the spectrum and the approximate spectrum of the completely nonnormalstrong Θ-operator identify and some K-groups of the C-algebra generated by this classoperator are computed in this part.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘The C~*-algebra generated by the strong Θ-operator is considered in this paper. Thepaper contains two parts. The first part shows that the commutant ideal I(T) of C(T) is*isomorphic to where ?_n ??_(n+1), n = 1,2,…and ?_n is * isomorphic to the n-matrix algebra over C_0(Z_0). In particular, when T is a completely nonnormal strong Θ-operator, I(T) is * isomorphic to C_0(Z_0)(×)K(I^2). The second part gives the equivalent con-ditions which make the spectrum and the approximate spectrum of the completely nonnormalstrong Θ-operator identify and some K-groups of the C-algebra generated by this classoperator are computed in this part.
