RANK-PRESERVING LINEAR MAPS ON B(X)

Let X be a Banach space with dimX>2 and B(X) the Banach algebra of all bounded linear operators on X. In recent years, some authors began to study the general linear maps on B(X), for example, discuss the representation of the spectrum-preserving or the commutativity-preserving linear maps on B(X). A few latest results in this field are as follows.