Jordan Isomorphisms on Nest Subalgebras

Aili Yang

doi:10.1155/2015/864792

Abstract

This paper is devoted to the study of Jordan isomorphisms on nest subalgebras of factor von Neumann algebras. It is shown that every Jordan isomorphismϕbetween the two nest subalgebrasalgMβandalgMγis either an isomorphism or an anti-isomorphism.

Highlights

Let A and B be two associative algebras
If M is a factor von Neumann algebra, it follows from [18] that DM(β) + RM(β) is weakly dense in algMβ
Throughout this paper, we assume that β and γ are nontrivial nests in a factor von Neumann algebra M and that φ : algMβ → algMγ is a Jordan isomorphism

Summary

Introduction

Let A and B be two associative algebras. A Jordan isomorphism φ from A onto B is a bijective linear map such that φ(T2) = φ(T)2 for every T ∈ A. If M is a factor von Neumann algebra, it follows from [18] that DM(β) + RM(β) is weakly dense in algMβ. Throughout this paper, we assume that β and γ are nontrivial nests in a factor von Neumann algebra M and that φ : algMβ → algMγ is a Jordan isomorphism.

Objectives

Results

Conclusion