Standard noncommuting and commuting dilations of commuting tuples

Bhat, Rajarama BV and Bhattacharyya, Tirthankar and Dey, Santanu (2003) Standard noncommuting and commuting dilations of commuting tuples. In: Transactions of the American Mathematical Society, 356 (4). pp. 1551-1568.

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Abstract

We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction, there are two commonly used dilations in multivariable operator theory. First there is the minimal isometric dilation consisting of isometries with orthogonal ranges, and hence it is a noncommuting tuple. There is also a commuting dilation related with a standard commuting tuple on boson Fock space. We show that this commuting dilation is the maximal commuting piece of the minimal isometric dilation. We use this result to classify all representations of the Cuntz algebra $O_n$ coming from dilations of commuting tuples.

Item Type:	Journal Article
Publication:	Transactions of the American Mathematical Society
Publisher:	American Mathematical Society
Additional Information:	Copyright of this article belongs to American Mathematical Society
Keywords:	Dilation;Commuting tuples;Complete positivity;Cuntz algebra
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/9332

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