Almost band preservers
Articles
Overview
published in
- POSITIVITY Journal
publication date
- December 2017
start page
- 1393
end page
- 1423
issue
- 4
volume
- 21
Digital Object Identifier (DOI)
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.
Classification
keywords
- banach lattice; band preserving operator; automatic continuity