On the closedness and self-adjointness of 3 x 3 operator matrices and application to a non-relativistic three-channel potential scattering model

摘要

In this paper, we are concerned with a 3 x 3 block operator matrices acting in a Banach or Hilbert space X-1 x X-2 x X-3 given by (A(1) A(2) A(3) B-1 B-2 B-3 C-1 C-2 C-3), where the linear entries are assumed to be unbounded. We study the closure as well as the self-adjointness in the case where the linear operators A(2) and A(3) are A(1)-bounded, B-1 and B-3 are B-2-bounded and C-1 and C-2 are C-3-bounded. These results are of importance to a non-relativistic three-channel potential scattering model.