Factorization of J-expansive meromorphic operator-valued functions

The factorization theorems are a generalization for J-biexpansive meromorphic operator-valued functions on an infinite-dimensional Hilbert space of the theorems on decomposition of J-expansive matrix functions on a finite-dimensional Hilbert space due to A. V. Efimov and V. P. Potapov Uspekhi Mat. Nauk28 (1973), 65–130; Trudy Moskov. Mat. Ob??.4 (1955), 125–236]. They also generalize theorems on factorization of J-expansive meromorphic operator functions due to Ju. P. Ginzburg Izv. Vys?. U?ebn. Zaved. Matematika32 (1963), 45–53]. Within the framework of generalized network theory, the results can be applied to the J-biexpansive real operators that characterize a Hilbert port. Application of the extraction procedure to a given real operator leads to its splitting into a product of real factors, corresponding to Hilbert ports of a simpler structure. This can be interpreted as an extension of the classical method of synthesis of passive n-ports by factor decomposition.