Some thoughts on Ando's theorem and Parrott's example

Bagchi, Bhaskar ; Bhattacharyya, Tirthankar ; Misra, Gadadhar (2002) Some thoughts on Ando's theorem and Parrott's example Linear Algebra and its Applications, 341 (1-3). pp. 357-367. ISSN 0024-3795

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In this short note, we present an elementary proof of Ando's theorem within a restricted class P of homomorphisms modeled after Parrott's example. We also show by explicit estimation that the cb-norm of the contractive homomorphism ρ of the tri-disc algebra, induced by the commuting triple of Parrott, exceeds 1. Indeed, we construct a polynomial P with matrix coefficients with the property ||ρ(P)||>||P||∞. In particular, we show that there are contractive homomorphisms of the tri-disc algebra which are not even 2-contractive.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Tri-Disk Algebra; Completely Contractive Homomorphism; cb-Norm
ID Code:1008
Deposited On:25 Sep 2010 11:22
Last Modified:16 May 2016 12:11

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