- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 1 Issue: 1
- On some Banach lattice-valued operators: A Survey
On some Banach lattice-valued operators: A Survey
Authors : Nutefe Kwami AGBEKO
Pages : 14-40
Doi:10.31197/atnaa.338349
View : 5 | Download : 2
Publication Date : 2017-09-30
Article Type : Other
Abstract :In 1928, at the International Mathematical Congress held in Bologna (Italy), Frigyes Riesz introduced the notion of vector lattice on function spaces and, talked about linear operators that preserve the join operation, nowadays known in the literature as Riesz homomorphisms (see [32]). In this survey we review the behaviors of some non-linear join-preserving Riesz space-valued functions, and we show how existing addition dependent results can be proved in these environments mutatis mutandis. (We kindly refer the reader to the papers [1, 2, 3, 4, 6, 7, 8, 9, 10, 5] for more information.)Keywords : Banach lattice-valued operators, , anach lattices, optimal measure, optimal average, dual Orlicz spaces, functional equation, functional inequality, Hyers-Ulam-Aoki type of stability,