Mappings that preserve pairs of operators with zero triple Jordan product Original Research Article

Let image be a field and ngreater-or-equal, slanted3. Suppose image contain all rank-one idempotents. The structure of surjections image satisfying ABA=0left right double arrowphi(A)phi(B)phi(A)=0 is determined. Similar results are also obtained for (a) subsets of bounded operators acting on a complex or real Banach space image, (b) the space of Hermitian matrices acting on n-dimensional vectors over a skew-field image, (c) subsets of self-adjoint bounded linear operators acting on an infinite dimensional complex Hilbert space. It is then illustrated that the results can be applied to characterize mappings phi on matrices or operators such thatimagefor functions F such as the spectral norm, Schatten p-norm, numerical radius and numerical range, etc.