Interpolation Theory and Its Applications pp 175-187 | Cite as

# Functions with an Operator Argument

## Abstract

In Chapters 1, 2 and 6 we deduced formulas expressing Φ_{1} by Φ_{2}. In the present chapter these formulas are interpreted in a new way. It is proved that the connection between Φ_{1} and Φ_{2} can be written in the form Φ_{1} = Ψ(*B*)Φ_{2} (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 [57] 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.

## Keywords

Commutation Relation Matrix Function Operator Identity Degenerate Case Interpolation Problem## Preview

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