  Let B(X) be the algebra of all bounded linear operators on a complex Banach
space X with dim X greater than 3. In this paper, we characterize the forms of
surjective linear maps on B(X) which preserve the dimension of the vector space
containing of all fixed points of operators, whenever X is a fifinite
dimensional Banach space. Moreover, we characterize the forms of linear maps on
B(X) which preserve the vector space containing of all fixed points of
operators.
