The Schur problem and block operator CMV matrices
Yury Arlinski\u{i}
TL;DR
This paper explores how CMV matrices and their sub-matrices can be used to describe all solutions to the Schur interpolation problem for contractive analytic operator-valued functions in the unit disk.
Contribution
It introduces a novel application of CMV matrices to characterize solutions of the Schur interpolation problem for operator-valued functions.
Findings
CMV matrices effectively describe all solutions to the Schur problem.
Sub-matrices of CMV matrices are instrumental in the solution characterization.
The approach unifies operator theory and matrix analysis in interpolation problems.
Abstract
The CMV matrices and their sub-matrices are applied to the description of all solutions to the Schur interpolation problem for contractive analytic operator-valued functions in the unit disk (the Schur class functions).
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