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 Є Z(E), the center of E.
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Huijsmans, C.B., De Pagter, B. (1992). Some Remarks on Disjointness Preserving Operators. In: Huijsmans, C.B., Luxemburg, W.A.J. (eds) Positive Operators and Semigroups on Banach Lattices. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2721-1_8
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DOI: https://doi.org/10.1007/978-94-017-2721-1_8
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