Additive maps preserving the fixed points of Jordan products of operators

Let \mathcal{B(X)} be the algebra of all bounded linear operators on a complex Banach space \mathcal{X}. In this paper, we determine the form of a surjective additive map \phi: \mathcal{B(X)} \rightarrow \mathcal{B(X)} preserving the fixed points of Jordan products of operators, i.e., F(AoB) \subseteq F(\phi(A) o\phi(B)), for every A,B \in \mathcal{B(X)}, where AoB=AB+BA, and F(A) denotes the set of all fixed points of operator A.

کلیدواژه ها:

Preserver problem ، Fixed point ، Jordan product