# 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 Copyright of this article belongs to Theta Foundation. Contractions;model theory;dilation;complete positivity. Division of Physical & Mathematical Sciences > Mathematics 22 Jul 2008 19 Sep 2010 04:47 http://eprints.iisc.ernet.in/id/eprint/15146