Jacobi Operators and Orthonormal Matrix-Valued Polynomials. II (original) (raw)

The study explores Jacobi operators within the context of self-adjoint operators on separable Hilbert spaces, highlighting their realization as block Jacobi operators. A significant contribution includes the construction of a system of orthogonal matrix-valued polynomials, linking these to spectral analysis and problems in moments. Further, the paper aims to establish connections between block Jacobi matrices and nonself-adjoint operators, enriching the understanding of these mathematical structures and their applications.