Functions with an Operator Argument
In Chapters 1, 2 and 6 we deduced formulas expressing Φ1 by Φ2. In the present chapter these formulas are interpreted in a new way. It is proved that the connection between Φ1 and Φ2 can be written in the form Φ1 = Ψ(B)Φ2 (11.0.1) where B is an operator argument of the matrix function Ψ(z) of the m x m order. With the help of formula (11.0.1) we manage to transfer partially the famous Sarason result  concerning commuting operators from the scalar case (m = 1) onto the matrix case (m > 1). Formula (11.0.1) also permits to obtain new results in the theory of operator factorization.
KeywordsCommutation Relation Matrix Function Operator Identity Degenerate Case Interpolation Problem
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