The Livšic function of a homogeneous symmetric operator and the multiplication theorem
摘要
This paper presents a solution to the Jørgensen–Muhly problem for a homogeneous symmetric operator with deficiency indices (1, 1) that does not admit a homogeneous self-adjoint extension. Based on the Livšic function approach, we characterize the set of all the solutions of the Jørgensen–Muhly problem up to unitary equivalence and describe the complete set of the corresponding unitary invariants.