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arXiv · 1610.02557

Almost band preservers

Timur Oikhberg·Pedro Tradacete
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Abstract

We study the stability of band preserving operators on Banach lattices. To this end the notion of $\varepsilon$-band preserving mapping is introduced. It is shown that, under quite general assumptions, a $\varepsilon$-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 $\varepsilon$-band preserving maps are also obtained.

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Timur Oikhberg, Pedro Tradacete. 2016-10-08. Almost band preservers. https://arxiv.org/abs/1610.02557

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