Maps Preserving Zero *-Products on B(H)

The conventional research topic in operator algebras involves exploring the structure of algebras and using homomorphic mappings to study the classification of algebras. In this study, a new invariant is developed based on the characteristics of the operator using the linear preserving method. The results show that the isomorphic mapping is used for preserving this invariant, which provides the classification information of operator algebra from a new perspective. Let H and kappa be Hilbert spaces with dimensions greater than two, and let B(H) and B(kappa) be the set of all bounded linear operators on H and kappa, respectively. For A, B is an element of B(H), the *, *-Lie, and *-Jordan products are defined by A*B, A*B - B*A, and A*B + B* A, respectively. Let Phi : B(H) -> B(kappa) be an additive unital surjective map. It is confirmed that if Phi preserves zero *, *-Lie, and *-Jordan products, then Phi is unitary or conjugate unitary isomorphisms.