On the fixed point spaces of some completely positive maps

Tomohiro Hayashi

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arXiv · 2103.04598

On the fixed point spaces of some completely positive maps

Tomohiro Hayashi

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Abstract

In this paper we generalize the results shown by Das and Peterson. Let $M$ be a ${\rm II}_1$-factor acting on $L^2(M)$. We consider certain unital normal completely positive maps on $B(L^2(M))$ which are identity on $M$. We investigate their fixed point spaces and obtain a rigidity result. As an application, we show some results of subfactors.

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Tomohiro Hayashi. 2021-03-08. On the fixed point spaces of some completely positive maps. https://arxiv.org/abs/2103.04598

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