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In this paper, we study the change of spectrum and the existence of Rieszbases of specific classes of $n\times n$ unbounded operator matrices, called:diagonally and off-diagonally generalized subordinate block operator matrices.An application to a $n\times n$ Gribov operator matrix acting on a sum ofBargmann spaces, illustrates the abstract results. As example, we consider aparticular Gribov operator matrix by taking special values of the realparameters of Pomeron.

On a Riesz Basis of Diagonally Generalized Subordinate Operator Matrices and Application to a Gribov Operator Matrix in Bargmann Space