A characterization of positive constrictive operators

Abstract

In this note we prove that if T is a positive operator on a real Banach lattice, then T is constrictive if and only if that T has the operator matrix decomposition \[ T = ( T 1 a m p ; 0 0 a m p ; T 2 ) , T = \left ( {\begin {array}{*{20}{c}} {{T_1}} & 0 \\ 0 & {{T_2}} \\ \end {array} } \right ), \] where T 1 {T_1} is a power-bounded generalized permutation matrix on a finite-dimensional space and T 2 n → 0 T_2^n \to 0 strongly.