Continuous orthosymmetric multilinear maps and homogeneous polynomials on Riesz spaces
Tóm tắt
We show that any continuous orthosymmetric multilinear map from an Archimedean Riesz space into a Hausdorff topological vector space is symmetric. Then, we establish a linear representation for continuous orthogonally additive homogeneous polynomials. This representation will be used to introduce and describe a new class of homogeneous polynomials, namely that of polyorthomorphisms. In particular, we prove that, for a Riesz space E and a natural number
$$n\ge 2$$
, the space
$${{\mathcal{P}}}_{orth}(^nE)$$
of all polyorthomorphisms of degree n is a Riesz space.
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