On some Banach lattice-valued operators: A Survey

Authors : Nutefe Kwami AGBEKO

Pages : 14-40

Doi:10.31197/atnaa.338349

View : 18 | Download : 5

Publication Date : 2017-09-30

Article Type : Review Paper

Abstract :In 1928, at the International Mathematical Congress held in Bologna insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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. insert ignore into journalissuearticles values(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,