On Some Linear Operators Preserving Disjoint Support Property

The aim of this work is to characterize all bounded linear operators $T:lpirightarrowlpi$ which preserve disjoint support property. We show that the constant coefficients of all isometries on $lpi$ are in the class of such operators, where $2neq pin [1,infty )$ and $I$ is a non-empty set. We extend preserving disjoint support property to linear operators on $mathfrak{c}_{0}(I).$ At the end, we obtain some equivalent properties of isometries on Banach spaces.