Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615800 | Journal of Mathematical Analysis and Applications | 2014 | 16 Pages |
Abstract
The goal of the paper is to extend the star order from associative algebras to non-associative Jordan Banach structures. Let A be a JBW algebra. We define a relation on A as the set of all pairs (a,b)âAÃA such that the range projections of a and bâa are orthogonal. We show that this relation defines a partial order on A which, in the case of the self-adjoint part of a von Neumann algebra, gives the star order. After showing basic properties of this order we shall prove the following preserver theorem: Let A be a JBW algebra without Type I2 direct summand and let Ï be a continuous map from A to B preserving the star order in both directions. If for each scalar λ one has Ï(λ1)=f(λ)z, where f is a (continuous) function and z is a central invertible element, then there is a unique Jordan isomorphism Ï:AâB such that Ï(a)=Ï(f(a))z. Moreover, we show that if A is a Type In factor, where nâ 2, then the equation above holds for all continuous maps preserving the star order in both directions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Martin Bohata, Jan Hamhalter,