Can you compute the operator norm?
Functional Analysis
2014-10-29 v2 Group Theory
Abstract
In this note we address various algorithmic problems that arise in the computation of the operator norm in unitary representations of a group on Hilbert space. We show that the operator norm in the universal unitary representation is computable if the group is residually finite-dimensional or amenable with decidable word problem. Moreover, we relate the computability of the operator norm on the product of non-abelian free groups to Kirchberg's QWEP Conjecture, a fundamental open problem in the theory of operator algebras.
Cite
@article{arxiv.1207.0975,
title = {Can you compute the operator norm?},
author = {Tobias Fritz and Tim Netzer and Andreas Thom},
journal= {arXiv preprint arXiv:1207.0975},
year = {2014}
}
Comments
15 pages, no figures; v2 is a slightly revised version