Centralizing additive maps on rank $ block triangular matrices

Let F be a field and let k, n1, . . . , nk be positive integers with n1 + · · · + nk = n > 2. We denote by Tn1,...,nk a block triangular matrix algebra over F with unity In and center Z(Tn1,...,nk ). Fixing an integer 1 1 upper triangular matrices over an arbitrary field is addressed.