Some new observations on interpolation in the spectral unit ball

dc.creatorBharali, Gautam
dc.date2007-04-16
dc.date2007-09-17
dc.date.accessioned2026-07-07T09:20:21Z
dc.date.available2026-07-07T09:20:21Z
dc.descriptionWe present several results associated to a holomorphic-interpolation problem for the spectral unit ball Ω_n, n\geq 2. We begin by showing that a known necessary condition for the existence of a $\mathcal{O}(D;Ω_n)$-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 Ω_n, n\geq 2.
dc.descriptionAdded 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
dc.identifierhttps://arxiv.org/abs/0704.1966
dc.identifierhttp://arxiv.org/abs/0704.1966
dc.identifierIntegral Equations Operator Theory 59 (2007) no. 3, 329-343
dc.identifierdoi:10.1007/s00020-007-1534-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154694
dc.subjectComplex Variables
dc.subjectOperator Algebras
dc.subject30E05, 47A56 (Primary); 32F45 (Secondary)
dc.titleSome new observations on interpolation in the spectral unit ball
dc.typetext

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