Mappings that preserve pairs of operators with zero triple Jordan productDobovišek, Mirko (Avtor) Kuzma, Bojan (Avtor) Lešnjak, Gorazd (Avtor) Li, Chi-Kwong (Avtor) Petek, Tatjana (Avtor) matrix algebraJordan triple productnonlinear preserversLet ▫$\mathbb{F}$▫ be a field and ▫$n \ge 3$▫. Suppose ▫${\mathfrak{G_1,G_2}} \subseteq M_n(\mathbb{F})▫$ contain all rank-one idempotents. The structure of surjections ▫$\phi : \mathfrak{G_1} \to \mathfrak{G_2}$▫ satisfying ▫$ABA = 0 \iff \phi(A)\phi(B)\phi(A) = 0$▫ is determined. Similar results are also obtained for (a) subsets of bounded operators acting on a complex or real Banach space, (b) the space of Hermitian matrices acting on ▫$n$▫-dimensional vectors over a skew-field, (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 that ▫$F(ABA) = F(\phi(A)\phi(B)\phi(A))▫$ for all ▫$A,B$▫ for functions ▫$F$▫ such as the spectral norm, Schatten ▫$p$▫-norm, numerical radius and numerical range, etc.20072016-04-08 16:41:27Delo ni kategorizirano7714ISSN: 0024-3795UDK: 512.552OceCobissID: 1119247COBISS.SI-ID: 11598870sl