**Spectrum of block-Jacobi operator – how to adopt some scalar Jacobi operator methods? **

The Block Jacobi operator J is an analog of the classical scalar Jacobi operator. This is a self-adjoint operator in the Hilbert space l^{2}(N, C^{d}) (instead of l^{2}(N, C)). Block Jacobi operator J is determined by a tridiagonal matrix with terms (“diagonals” and “weights”) being d✕d “blocks” — d by d matrices (instead of scalar terms for the scalar Jacobi operator case).

When d>1 the spectral analysis of J makes much more difficult than in the scalar case d = 1, especially when we study unbounded block-weights.

During my talk I will explain some technical details of such problems. I will also formulate some conjectures and open questions.