## Access

You are not currently logged in.

Access JSTOR through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# A MODEL THEORY FOR q-COMMUTING CONTRACTIVE TUPLES

B.V. RAJARAMA BHAT and TIRTHANKAR BHATTACHARYYA
Journal of Operator Theory
Vol. 47, No. 1 (Winter 2002), pp. 97-116
Stable URL: http://www.jstor.org/stable/24715527
Page Count: 20
Preview not available

## Abstract

A contractive tuple is a tuple (T1,..., Td) of operators on a common Hilbert space such that (0.1) ${\mathrm{T}}_{1}{\mathrm{T}}_{1}^{*}+\cdot \cdot \cdot +{\mathrm{T}}_{\mathrm{d}}{\mathrm{T}}_{\mathrm{d}}^{*}\le 1$. It is said to be q-commuting if TjTi = qijTiTj for all 1 ≤ i < j ≤ d, where qij, 1 ≤ i < j ≤ 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.

• [97]
• 98
• 99
• 100
• 101
• 102
• 103
• 104
• 105
• 106
• 107
• 108
• 109
• 110
• 111
• 112
• 113
• 114
• 115
• 116