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arXiv · 2610.41746

A solution to Haagerup's Problem on decomposable maps

Rui Okayasu
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Abstract

We prove that a von Neumann algebra $N$ is injective if and only if $\|T\|_{\mathrm{dec}}=\|T\|_{\mathrm{cb}}$ for every linear map $T:\ell^\infty_3to N$, answering a problem of Haagerup (1985).

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Rui Okayasu. 2026-10-30. A solution to Haagerup's Problem on decomposable maps. https://arxiv.org/abs/2610.41746

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