Functions with an Operator Argument

  • L. A. Sakhnovich
Part of the Mathematics and Its Applications book series (MAIA, volume 428)

Abstract

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(B2 (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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • L. A. Sakhnovich
    • 1
  1. 1.Ukrainian State Academy of CommunicationOdessaUkraine

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