Abstract:
In this paper, we study the operators generated by infinite tridiagonal block matrices under the condition that the spectrum of the corresponding diagonal matrix is separated. Using the method of similar operators, we obtain conditions that provide the diagonalizability of the original operator (or its block diagonalizability). Also, we obtain the asymptotics of the weighted means of the eigenvalues of such operators.
Keywords:eigenvalue, method of similar operators, infinite block tridiagonal matrix.