On doubly commuting operators in C1,r class and quantum annulus
Abstract
For r between 0 and 1, let Ar={z∈C:r<|z|<1}. We study the class C1,r={T:T is invertible and ∥T∥,∥rT−1∥⩽1}. The class C1,r is closely related to the \textit{quantum annulus} given by QAr={T:T is invertible and ∥rT∥, ∥rT−1∥⩽1}. McCullough and Pascoe proved that T∈QAr dilates to an operator S satisfying (r−2+r2)I−S∗S−S−1S−∗=0. We extend this dilation result to doubly commuting tuples of operators in quantum annulus as well as in C1,r class. We also provide characterizations and decomposition results for such tuples.
Fields of Study & Subjects
Advanced Operator Algebra Research
Spectral Theory in Mathematical Physics
Holomorphic and Operator Theory
Publication details
- Journal / source
- Journal of Operator Theory
- Publisher
- Theta Foundation
- Volume
- 96
- Issue
- 1
- Pages
- 277–294
- Publication date
- 8 August 2026
- Language
- EN