On the fixed point spaces of some completely positive maps

TL;DR

This paper investigates fixed point spaces of certain unital completely positive maps on operator algebras, extending previous results and applying findings to subfactor theory.

Contribution

It generalizes prior work by Das and Peterson on fixed point spaces of completely positive maps in the context of ${ m II}_1$-factors.

Findings

Identifies conditions for fixed point space rigidity.

Provides new insights into subfactor structures.

Extends understanding of completely positive maps on operator algebras.

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.