Deficiency numbers of symmetric operators generated by block Jacobi matrices

Abstract

Symmetric block Jacobi matrices and the corresponding symmetric operators are studied. Let be the size of the blocks in the matrix . As is known, the deficiency numbers and of the operator satisfy the inequalities and achieve their maximum value simultaneously. Let and be arbitrary integers such that . It is shown that there exists a symmetric Jacobi matrix such that and are the deficiency numbers of the corresponding symmetric operator .