Access

You are not currently logged in.

Access JSTOR through your library or other institution:

login

Log in through your 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
Published by: Theta Foundation
Stable URL: http://www.jstor.org/stable/24715527
Page Count: 20
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
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
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.

Page Thumbnails

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