Some new observations on interpolation in the spectral unit ball
Abstract
We present several results associated to a holomorphic-interpolation problem for the spectral unit ball \Omega_n, n\geq 2. We begin by showing that a known necessary condition for the existence of a -interpolant (D here being the unit disc in the complex plane), given that the matricial data are non-derogatory, is not sufficient. We provide next a new necessary condition for the solvability of the two-point interpolation problem -- one which is not restricted only to non-derogatory data, and which incorporates the Jordan structure of the prescribed data. We then use some of the ideas used in deducing the latter result to prove a Schwarz-type lemma for holomorphic self-maps of \Omega_n, n\geq 2.
Cite
@article{arxiv.0704.1966,
title = {Some new observations on interpolation in the spectral unit ball},
author = {Gautam Bharali},
journal= {arXiv preprint arXiv:0704.1966},
year = {2008}
}
Comments
Added a definition (Def.1.1); 2 of the 4 results herein are minor refinements of those in the author's preprint math.CV/0608177; to appear in Integral Eqns. Operator Theory