Weak Adjoint-preserving Liner Operators On Upper Triangular Matrix Space

In this thesis, we introduce the background and the development of Preserver Problems firstly, then we study the liner map of preserving weak adjoint matrices of upper triangular matrices on upper triangular matrices space. Finally we obtain the following main result.Let∫be a liner map of preserving weak adjoint matrices and satisfying that f(Ein)≠0on upper triangular matrices space. Then there exists an invertible matrix P∈Tn(F), such that or for all A∈Tn(F), where cn-2=1.