Operator Identities and S-nodes

Abstract

In this chapter we continue the study of the operator identities that arose in connection with factorization problems in Chapter 1. These identities lead to the notion of an S-node, which is a generalization of the notion of node or colligation [58], [14] known in the theory of characteristic functions of operators. We shall focus on the operator identities that generate symmetric S-nodes. In this way we obtain new results and recover previously known results [65] on hereditary properties of factors arising in the factorization of an operator-valued function.