Generalized Toeplitz Plus Hankel Operators: Kernel Structure and Defect Numbers

摘要

Generalized Toeplitz plus Hankel operators T (a) + Ha(b) generated by functions a, b and a linear fractional Carleman shift a changing the orientation of the unit circle T are considered on the Hardy spaces H p(T), 1 < p < 8. If the functions a, b. L8(T) and satisfy the condition the defect numbers of the operators T (a) + Ha(b) are established and an explicit description of the structure of the kernels and cokernels of the operators mentioned is given.