Abstract
In this note we present a simple proof of the following results: if T: E → E is a lattice homomorphism on a Banach lattice E, then: i) σ(T)={1} implies T=I; and ii) r(T−I)<1 implies T∈Z(E), the center of E.
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Huijsmans, C.B., De Pagter, B. Some remarks on disjointness preserving operators. Acta Appl Math 27, 73–78 (1992). https://doi.org/10.1007/BF00046638
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DOI: https://doi.org/10.1007/BF00046638