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arXiv · 1207.0975

Can you compute the operator norm?

Tobias Fritz·Tim Netzer·Andreas Thom
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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.

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Tobias Fritz, Tim Netzer, Andreas Thom. 2012-07-04. Can you compute the operator norm?. https://doi.org/10.1090/s0002-9939-2014-12170-8

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