ON AN INFINITE DIMENSIONAL LESLIE MATRIX IN THE BANACH SPACE c_0

In this paper, we introduce Leslie matrix with an infinite dimensional components. The top row {α_n } ^∞_1 a and sub diagonal {w_n }^∞_1 such matrix are assumed to be elements of the Banach space c_0 .We prove that an infinite dimensional Leslie matrices have a positive real eigenvalue. In addition such matrix defines a compact linear operator from c_0 into c_0 .