2016/10/08 by Timur Oikhberg, Oikhberg, Timur, Pedro Tradacete +1
Mathematics · Computer Science · #Advanced Banach Space Theory #Advanced Algebra and Logic #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1610.02557
We study the stability of band preserving operators on Banach lattices. To this end the notion of ε-band preserving mapping is introduced. It is shown that, under quite general assumptions, a ε-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 ε-band preserving maps are also obtained.