Can you compute the operator norm?

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.

15 pages, no figures; v2 is a slightly revised version

References in corpus (2)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Convergence of SDP hierarchies for polynomial optimization on the hypersphere

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