2×2阶上三角型算子矩阵的可能谱

Let H1 and H2 be infinite dimensional complex separable Hilbert space, we denote by MC the upper triangular operator matrix acting on H1 . H2 of the form MC= A C 0 B !. For given operators A 2 B(H1) and B 2 B(H2), the sets S C2B(H2,H1) .r(MC) and S C2B(H2,H1) .c(MC) are completely characterized, where .r(T), .c(T) and B(H2,H1) denote the continuous spectrum, residual spectrum of an operator T, and the set of all the bounded linear operators from H2 into H1, respectively.