Additivity of Jordan elementary maps on nest algebras Original Research Article

Let image be a standard subalgebra of a nest algebra on a Hilbert space of dimension greater than one and image an arbitrary algebra. A Jordan elementary map of image is a pair (M, M*) where image and image are two maps satisfyingimageforimage, image. In this note, it is proved that for a special class of surjective Jordan elementary maps of image, every member in it is automatically additive. Also, we construct a counterexample which shows that this result is not necessarily true for all surjective Jordan elementary maps.