A characterization of positive constrictive operators

Du, Hong Ke

doi:10.1090/S0002-9939-1994-1185265-0

A characterization of positive constrictive operators
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Proc. Amer. Math. Soc. 121 (1994), 755-759 Request permission

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 \[ T = \left ( {\begin {array}{*{20}{c}} {{T_1}} & 0 \\ 0 & {{T_2}} \\ \end {array} } \right ),\] where ${T_1}$ is a power-bounded generalized permutation matrix on a finite-dimensional space and $T_2^n \to 0$ strongly.

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Introduction to advance mathematics

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