Almost band preservers

DOI10.1007/S11117-017-0475-ZarXiv1610.02557MaRDI QIDQ6278426

Pedro Tradacete, T. Oikhberg

Publication date: 8 October 2016

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.

Mathematics Subject Classification ID

Banach lattices (46B42) Linear operators on function spaces (general) (47B38)

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