Criteria of unitary equivalence of Hermitian operators with a degenerate spectrum

Nonimprovable, in general, estimates of the number of necessary and sufficient conditions for two Hermitian operators to be unitarily equaivalent in a unitary space are obtained when the multiplicities of eigenvalues of operators can be more than 1. The explicit form of these conditions is given. In the Appendix the concept of conditionally functionally independent functions is given and the corresponding necessary and sufficient conditions are presented.