Complete Indefiniteness Tests for Jacobi Matrices with Matrix Entries

AbstractWe study the problem concerning the maximality of the deficiency indices of operators generated by symmetric Jacobi matrices with matrix entries in the space $$\user1{l}_2$$ . Effective conditions for the maximality of the deficiency indices are given in terms of entries of the Jacobi matrix. These conditions are new even in the scalar (one-dimensional) case.