Inverses of Toeplitz plus Hankel operators with generating matrix functions

The invertibility of Toeplitz plus Hankel operators T(A) + H(B), A, B is an element of L-dxd(infinity)(T) acting on vector Hardy spaces H-d(p)(T), 1 < p < infinity, is studied. Assuming that the generating matrix functions A and B satisfy the equation B(-1)A = (A) over tilde (-1)(B) over tilde, where (A) over tilde (t) := A(1/t), (B) over tilde (t) := B(1/t), t is an element of T, we establish sufficient conditions for the one-sided invertibility and invertibility of the operators mentioned and construct the corresponding inverses. If d = 1, the above equation reduces to the known matching condition, widely used in the study of Toeplitz plus Hankel operators with scalar generating functions.