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

Abstract

We investigate various notions of peaking behaviour for states on a ${\mathrm{C}}^{\ast }$-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 ${\mathrm{C}}^{\ast }$-algebra at a given state, and use this localization procedure to verify a variation of Arveson's hyperrigidity conjecture for arbitrary operator systems.

26 pages. Version 2, to appear in the Proceedings of the London Mathematical Society

References in corpus (1)

• Multiplier algebras of complete Nevanlinna-Pick spaces: dilations, boundary representations and hyperrigidity

Cited by in corpus (2)

• Strongly peaking representations and compressions of operator systems
• Rational Cuntz states peak on the free disk algebra