Geometric Dilations and Operator Annuli

Abstract

Fix 1<R. The dilation theory for the quantum annulus, consisting of those invertible Hilbert space operators T such that the norm of T and its inverse are both at most R 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.

V2. Corrected the attribution for Theorem 1.2. V3. Corrected the proof of Theorem 1.1(c) plus some minor fixes. V4 A few typos fixed and several small expository upgrades