Deficiency numbers of operators generated by infinite Jacobi matrices

Abstract

New conditions for minimality, maximality, and nonmaximality of deficiency numbers of the minimal operator generated by the infinite Jacobi matrix with m × m matrix entries in the Hilbert space of mdimensional vectors are presented. Special attention is given to the case m = 1, i.e., to conditions on the elements of a tridiagonal numerical Jacobi matrix under which the determinate case of the classical power moment problem is realized.