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arXiv · 2406.05302

On a question of Blecher, Pisier, Shlyakhtenko

Roy Araiza·Marius Junge·Carlos Palazuelos
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Abstract

We show the failure of a matricial version of Grothendieck's theorem for operator spaces, thereby resolving a long-standing open question in the field. Moreover, by showing that such a counterexample can occur in the simplest context of commutative $C^*$-algebras, we address some other open questions in operator algebras. Our constructions, completely explicit and fairly simple, are inspired by some techniques in quantum information theory.

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Roy Araiza, Marius Junge, Carlos Palazuelos. 2024-06-08. On a question of Blecher, Pisier, Shlyakhtenko. https://arxiv.org/abs/2406.05302

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