Curvature colligations (Q788257)

This paper is a continuation of [Toeplitz centennial, Toeplitz Mem. Conf., Tel Aviv 1981, Operator Theory, Adv. Appl. 4, 271-302 (1982; Zbl 0485.47028); Integral Equations Oper. theory 6, 31-58 (1983; Zbl 0516.46050); ibid. 6, 184-205 (1983; Zbl 0516.46051)]. It is shown that the curvature operators of a connection colligation may be included in a natural way in an operator colligation. This operator colligation is called the curvature colligation. As an application it is shown that if several operators are included in an operator colligation, then all their commutators may be included in a natural way in a new operator colligation. In particular a notion of the commutator of two operator colligations is obtained.