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.
DOI: http://dx.doi.org/10.7900/jot.2013jun10.2002
Keywords: Schur class functions, operator pre-order, operator
equivalence relation, linear fractional transformations
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