# Some thoughts on Ando’s theorem and Parrott’s example

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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## Abstract

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 Copyright of this article belongs to Elsevier Tri-disk algebra;Completely contractive homomorphism;cb-norm Division of Physical & Mathematical Sciences > Mathematics 30 Nov 2007 19 Sep 2010 04:33 http://eprints.iisc.ernet.in/id/eprint/9350