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Factorization of multilinear operators defined on products of function spaces. (English) Zbl 07506360

The author obtain strong and interesting results where introduced the factorization of multilinear operators defined on topological product of particular function spaces through a generic continuous multilinear operator. As application, lattice geometric inequalities and integral representations are obtained and some isometries between product factorable multilinear maps and orthogonally additive polynomials are presented.

MSC:

47H60 Multilinear and polynomial operators
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47B38 Linear operators on function spaces (general)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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