FACTORIZATION FORMULAS FOR SOME CLASSES OF GENERALIZED J-INNER MATRIX VALUED FUNCTIONS

The class U-kappa(j(pq)) of generalized j(pq)-inner matrix valued functions (mvf's) was introduced in [2]. For a mvf W from a subclass U-kappa(r) (j(pq)) of U kappa(j(pq)) the notion of the right associated pair was introduced in [13] and some factorization formulas were found. In the present paper we introduce a dual subclass U-kappa(l)(j(pq)) and for every mvf W epsilon U-kappa(l) (j(pq)) a left associated pair {beta(1), beta(2)} is defined and factorization formulas for W in terms of beta(1), beta(2) are found. The notion of a singular generalized j(pq)-inner mvf W is introduced and a characterization of singularity of W is given in terms of associated pair.