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Can you compute the operator norm?


Authors: Tobias Fritz, Tim Netzer and Andreas Thom
Journal: Proc. Amer. Math. Soc. 142 (2014), 4265-4276
MSC (2010): Primary 43A20
DOI: https://doi.org/10.1090/S0002-9939-2014-12170-8
Published electronically: August 7, 2014
MathSciNet review: 3266994
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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 a 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 a decidable word problem. Moreover, we relate the computability of the operator norm on the group $ F_2 \times F_2$ to Kirchberg's QWEP Conjecture, a fundamental open problem in the theory of operator algebras.


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Additional Information

Tobias Fritz
Affiliation: Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5
Email: tfritz@perimeterinstitute.ca

Tim Netzer
Affiliation: University of Leipzig, PF 100920, 04009 Leipzig, Germany
Email: tim.netzer@math.uni-leipzig.de

Andreas Thom
Affiliation: University of Leipzig, PF 100920, 04009 Leipzig, Germany
Email: andreas.thom@math.uni-leipzig.de

DOI: https://doi.org/10.1090/S0002-9939-2014-12170-8
Received by editor(s): July 12, 2012
Received by editor(s) in revised form: January 15, 2013
Published electronically: August 7, 2014
Communicated by: Marius Junge
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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