On Some Linear Operators Preserving Disjoint Support Property

The aim of this work is to characterize all bounded linear operators $T:\lpi\rightarrow\lpi$ which preserve disjoint support property. We show that the constant coefficients of all isometries on $\lpi$ are in the class of such operators, where $2\neq p\in [1,\infty )$ 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.