Jordan Isomorphisms on Nest Subalgebras

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.

Germán Ancochea's work on projectivities, harmonicity preservers and semi-homomorphisms

“…Jordan homomorphisms between other kinds of rings have been thoroughly investigated. We refer to J. H. Zhang [170], K. I. Beidar, M. Brešar and M. A. Chebotar [17], F. Lu [116], F. Lu and T.-L. Wong [165], A. L. Yang and J. H. Zhang [168], F. Kuzucuoglu and V. M. Levchuk [102], J. Alaminos, J. Extremera and A. R. Villena [2], E. Akkurt, M. Akkurt and G. P. Barker [1], A. L. Yang [167], R. Brusamarello, E. Z. Fornaroli and M. Khrypchenko [39].…”