An addendum to the multiplication and factorization theorems of brodskiǐ—livšic—potapov

Abstract

In this paper the classical Brodskiǐ—Livšic— operator colligation is generalized to certain pairs of bounded linear operators and the corresponding characteristic operator—valued (transfer) function is introduced. The fundamental results due to M.S. Brodskiǐ, M.S. Livšic, and V.P. Potapov are then extended to such colligations. These new types of colligations can be used to obtain, for instance, realization results for general Herglotz—Nevanlinna functions.

Keywords:

• Operator colligation
• characteristic (transfer) function
• multiplication and factorization of colligations

AMS:

• 47A10
• 47B44
• 46E20
• 46F05