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arXiv · 1709.01649

Non-commutative peaking phenomena and a local version of the hyperrigidity conjecture

Raphaël Clouâtre
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Abstract

We investigate various notions of peaking behaviour for states on a $\mathrm{C}^*$-algebra, where the peaking occurs within an operator system. We pay particularly close attention to the existence of sequences of elements forming an approximation of the characteristic function of a point in the state space. We exploit such characteristic sequences to localize the $\mathrm{C}^*$-algebra at a given state, and use this localization procedure to verify a variation of Arveson's hyperrigidity conjecture for arbitrary operator systems.

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Raphaël Clouâtre. 2017-09-06. Non-commutative peaking phenomena and a local version of the hyperrigidity conjecture. https://doi.org/10.1112/plms.12133

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