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 |
---|---|

Publication: | Linear Algebra and its Applications |

Publisher: | Elsevier |

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 |

URI: | http://eprints.iisc.ac.in/id/eprint/9350 |

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