On an Infinite Dimensional Leslie Matrix in The Banach Space C0

Abstract

In this paper, we introduce Leslie matrix with an infinite dimensional components. The top row {α_n}^∞₁  and sub diagonal {⍵_n}^∞₁ of such matrix are assumed to be elements of the Banach space c₀ .We prove that an infinite dimensional Leslie matrices have a positive real eigenvalue. In addition such matrix defines a compact linear operator from c₀ into c₀.

Keywords: Leslie Matrix, Infinite Population, Null Sequences, Eigenvalues.

2000 Mathematics Subject Classification: Primary 05C38; secondary 05C35