Bagchi, Bhaskar and Bhattacharyya, Tirthankar and Misra, Gadadhar (2002) Some thoughts on Ando’s theorem and Parrott’s example. In: Linear Algebra and its Applications, 341 (1-3). pp. 357-367.
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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 /rho 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 \parallel \rho (P)\parallel >\parallel P\parallel \infty. In particular, we show that there are contractive homomorphisms of the tri-disc algebra which are not even 2-contractive.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Elsevier|
|Keywords:||Tri-disk algebra;Completely contractive homomorphism;cb-norm|
|Department/Centre:||Division of Physical & Mathematical Sciences > Mathematics|
|Date Deposited:||30 Nov 2007|
|Last Modified:||19 Sep 2010 04:33|
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