Previous issue ·  Next issue ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

Journal of Operator Theory

Volume 72, Issue 2, Fall 2014  pp. 487-520.

A pre-order and an equivalence relation on Schur class functions and their invariance under linear fractional transformations

Authors:  S. ter Horst
Author institution: Unit for Business Mathematics and Informatics, North-West University, Potchefstroom, 2531, South Africa

Summary:  Motivated by work of Yu.L. Shmul'yan a pre-order and an equivalence relation on the set of operator-valued Schur class functions are introduced and the behavior of Redheffer linear fractional transformations (LFTs) with respect to these relations is studied. In particular, it is shown that Redheffer LFTs preserve the equivalence relation, but not necessarily the pre-order. The latter does occur under some additional assumptions on the coefficients in the Redheffer LFT.

Keywords:  Schur class functions, operator pre-order, operator equivalence relation, linear fractional transformations

Contents   Full-Text PDF