A Model Theory For $q$-Commuting Contractive Tuples

Bhat, Rajarama BV and Bhattacharyya, Tirthankar (2002) A Model Theory For $q$-Commuting Contractive Tuples. In: Journal of Operator Theory, 47 (1). pp. 97-116.

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Abstract

A contractive tuple is a tuple $(T_1, \ldots , T_d)$ of operators on a common Hilbert space such that $T_1T_1^* + \cdots + T_dT_d^* \leq 1$. It is said to be $q$-commuting if $T_jT_i = q_{ij}T_iT_j$ for all $1 \leq i < j \leq d$, where $q_{ij}$, $1\leq i<j\leq d$ are complex numbers. These are higher-dimensional and non-commutative generalizations of a contraction. A particular example of this is the $q$-commuting shift. In this note, we investigate model theory for q-commuting contractive tuples using representations of the $q$-commuting shift.

Item Type:	Journal Article
Publication:	Journal of Operator Theory
Publisher:	Theta Foundation
Additional Information:	Copyright of this article belongs to Theta Foundation.
Keywords:	Contractions;model theory;dilation;complete positivity.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	22 Jul 2008
Last Modified:	19 Sep 2010 04:47
URI:	http://eprints.iisc.ac.in/id/eprint/15146

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