Almost band preservers

Timur Oikhberg, Pedro Tradacete

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1393-1423
Number of pages31
JournalPositivity
Volume21
Issue number4
DOIs
StatePublished - Dec 1 2017

Keywords

  • Automatic continuity
  • Banach lattice
  • Band preserving operator

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Mathematics(all)

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