On some Banach lattice-valued operators: A Survey

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;

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