Geometric Dilations and Operator Annuli

Abstract

Fix 0 < r < 1. The dilation theory for the quantum annulus QA r , consisting of those invertible Hilbert space operators T satisfying T , T −1 ≤ r −1 , is determined. The proof technique involves a geometric approach to dilation that applies to other well known dilation theorems. The dilation theory for the quantum annulus is compared, and contrasted, with the dilation theory for other canonical operator annuli.