On a von Neumann algebra which is a complemented subspace

2013/12/02 by Christensen, Erik, Wang, Liguang
#46L10 #46L50 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1312.0450

Abstract

Let M be a von Neumann algebra of type II₁ which is also a complemented subspace of B(H). We establish an algebraic criterion, which ensures that M is an injective von Neumann algebra. As a corollary we show that if M is a complemented factor of type II₁ on a Hilbert space H, then M is injective if its fundamental group is non-trivial.

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