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:99506
Deposited On:27 Nov 2016 12:53
Last Modified:29 Nov 2016 09:34

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