- POSITIVITY Journal
- December 2017
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- We study the stability of band preserving operators on Banach lattices. To this end the notion of -band preserving mapping is introduced. It is shown that, under quite general assumptions, a -band preserving operator is in fact a small perturbation of a band preserving one. However, a counterexample can be produced in some circumstances. Some results on automatic continuity of -band preserving maps are also obtained.
- banach lattice; band preserving operator; automatic continuity