Symmetric Operator Space Preservation In Banach Algebra Invariant

Let H be an infinite dimensional complex Hilbert space, B(H] the Banach algebra of all bounded linear operators on H, and S(H) the space of all symmetric operators on H.Let L be a real linear, weakly continuous rank one preserver of S(H). In this paper, we determined the form of L. Then we get the forms of rank-preserving by using rank one preservers.