Date:
Wed, 03/04/201912:00-13:00
Location:
Ross 70
Title:
Dilations of q-commuting unitaries
Abstract:
Let (u,v) be a pair of unitary operators on a Hilbert space H such that vu=quv for a complex number q of modulus 1. For q' another complex number of modulus 1, we determine the smallest constant c>0 for which there exists a pair of q' commuting unitaries (U,V) on a larger Hilbert space K containing H such that (u,v) is the compression of (cU,cV) to H.
It turns out that these constants are closely related to the norm of almost Mathieu operators and that the developed techniques can be used to give new simplified proofs of the continuity of the spectra of almost Mathieu operators and of the field of rotation C*-algebras.
Joint work with Orr Shalit.
Dilations of q-commuting unitaries
Abstract:
Let (u,v) be a pair of unitary operators on a Hilbert space H such that vu=quv for a complex number q of modulus 1. For q' another complex number of modulus 1, we determine the smallest constant c>0 for which there exists a pair of q' commuting unitaries (U,V) on a larger Hilbert space K containing H such that (u,v) is the compression of (cU,cV) to H.
It turns out that these constants are closely related to the norm of almost Mathieu operators and that the developed techniques can be used to give new simplified proofs of the continuity of the spectra of almost Mathieu operators and of the field of rotation C*-algebras.
Joint work with Orr Shalit.