Redheffer representations and relaxed commutant lifting
Abstract
It is well known that the solutions of a (relaxed) commutant lifting problem can be described via a linear fractional representation of the Redheffer type. The coefficients of such Redheffer representations are analytic operator-valued functions defined on the unit disc D of the complex plane. In this paper we consider the converse question. Given a Redheffer representation, necessary and sufficient conditions on the coefficients are obtained guaranteeing the representation to appear in the description of the solutions to some relaxed commutant lifting problem. In addition, a result concerning a form of non-uniqueness appearing in the Redheffer representations under consideration and an harmonic maximal principle, generalizing a result of A. Biswas, are proved. The latter two results can be stated both on the relaxed commutant lifting as well as on on the Redheffer representation level.
Cite
@article{arxiv.0906.0971,
title = {Redheffer representations and relaxed commutant lifting},
author = {S. ter Horst},
journal= {arXiv preprint arXiv:0906.0971},
year = {2020}
}
Comments
19 pages