ORTHOGONALITY PRESERVERS REVISITED
Abstract
We obtain a complete characterization of all orthogonality preserving operators from a JB*-algebra to a JB*-triple. If T : J → E is a bounded linear operator from a JB*-algebra (respectively, a C*-algebra) to a JB*-triple and h denotes the element T**(1), then T is orthogonality preserving, if and only if, T preserves zero-triple-products, if and only if, there exists a Jordan *-homomorphism 
such that S(x) and h operator commute and T(x) = h•r(h) S(x), for every x ∈ J, where r(h) is the range tripotent of h, 
is the Peirce-2 subspace associated to r(h) and •r(h) is the natural product making 
a JB*-algebra.
This characterization culminates the description of all orthogonality preserving operators between C*-algebras and JB*-algebras and generalizes all the previously known results in this line of study.
The authors were partially supported by I+D MEC project no. MTM2008-02186, and Junta de Andalucía grants FQM0199 and FQM3737.
To the memory of Issac Kantor
