Abstract. The aim of this article is to prove a representation theorem for orthogonally additive polynomials in the spirit of the recent theorem on representation of orthogonally additive polynomials on Banach lattices but for the setting of Riesz spaces. To this purpose the notion of p-orthosymmetric multilinear form is introduced and it is shown to be equivalent to the orthogonally additive property of the corresponding polynomial. Then the space of positive orthogonally additive polynomials on an Archimedean Riesz space taking values on an uniformly complete Archimedean Riesz space is shown to be isomorphic to the space of positive linear forms on the n-power in the sense of Boulabiar and Buskes of the original Riesz space.
In this paper we show that the Aron-Berner type extension of polynomials preserves the P -continuity property. To this end we introduce a new version of Goldstine's Theorem for locally complemented subspaces.
ABSTRACT. Leí X be a completely regular Hausdorff space and C(X) the algebra of alí continuous <-valued functions on X ([4] can be found conditions on A under whicls cadi character of A, i.e., each non-zero 1K-linear multiplicative funclional 4xA-* 1K, is given by a point evaluation al sorne point of X.In ibis paper we presení a «Michael» type theorem for the particular case in which X is a real Banach space. As consequence it is showed thai if E is a separable Banach space or E is the topological dual space of a separable Banach space aud A ís the algebra of ah real analytic or the algebra of alí real Cm.functions, ni = 0, 1 oD, on E, then every character 4 of A is a point evaluation at sorne poiní of E.
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