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 n, n≥ 2. We begin by showing that a known necessary condition for the existence of a O(D;n)-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 n, n≥ 2.
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