Extensions of the symmetric operator generated by an infinite Jacobi matrix

A space of boundary values is constructed for minimal symmetric operator in ℓC2(N;E) (N:= {0,1,2,…}, dim E = n < ∞), with maximal deficiency indices (n, n), generated by an infinite Jacobi matrix with matrix entries. A description of all maximal dissipative, maximal accretive, selfadjoint, and other extensions of such a symmetric operator is given in terms of boundary conditions at infinity.