Intersecting Jones projections
算子代数
2018-10-16 v1
摘要
Let M be a von Neumann algebra on a Hilbert space H with a cyclic and separating unit vector \Omega and let \omega be the faithful normal state on M given by \omega(\cdot)=(\Omega,\cdot\Omega). Moreover, let {N_i :i\in I} be a family of von Neumann subalgebras of M with faithful normal conditional expectations E_i of M onto N_i satisfying \omega=\omega\circ E_i for all i\in I and let N=\bigcap_{i\in I} N_i. We show that the projections e_i, e of H onto the closed subspaces \bar{N_i\Omega} and \bar{N\Omega} respectively satisfy e=\bigwedge_{i\in I}e_i.This proves a conjecture of V.F.R. Jones and F. Xu in \cite{JonesXu04}.
引用
@article{arxiv.math/0412457,
title = {Intersecting Jones projections},
author = {Sebastiano Carpi},
journal= {arXiv preprint arXiv:math/0412457},
year = {2018}
}