1991/05/31 by Gilles Pisier, Pisier, Gilles
Mathematics · #46L #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L
paper · pdf · doi:10.48550/arxiv.math/9201227
arxiv created 1991/05/31 · openalex publication_date 1991/05/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we include two remarks about bounded (\underlinenot necessarily contractive) linear projections on a von Neumann-algebra. We show that if M is a von Neumann-subalgebra of B(H) which is complemented in B(H) and isomorphic to M ⊗ M then M is injective (or equivalently M is contractively complemented). We do not know how to get rid of the second assumption on M. In the second part,we show that any complemented reflexive subspace of a C^*- algebra is necessarily linearly isomorphic to a Hilbert space.