Almost band preservers Articles uri icon

authors

  • OIKHBERG, TIMUR
  • TRADACETE PEREZ, PEDRO

publication date

  • December 2017

start page

  • 1393

end page

  • 1423

issue

  • 4

volume

  • 21

International Standard Serial Number (ISSN)

  • 1385-1292

Electronic International Standard Serial Number (EISSN)

  • 1572-9281

abstract

  • 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.

keywords

  • banach lattice; band preserving operator; automatic continuity