Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498371 | Linear Algebra and its Applications | 2005 | 12 Pages |
Abstract
Let A be a standard subalgebra of a nest algebra on a Hilbert space of dimension greater than one and B an arbitrary algebra. A Jordan elementary map of AÃB is a pair (M, M*) where M:AâB and Mâ:BâA are two maps satisfyingM(AMâ(B)A)=M(A)BM(A),Mâ(BM(A)B)=Mâ(B)AMâ(B)forAâA, BâB. In this note, it is proved that for a special class of surjective Jordan elementary maps of AÃB, 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Pengtong Li, Fangyan Lu,