We prove that every multipolynomial between Banach spaces is the composition of a canonical multipolynomial with a linear operator, and that this correspondence establishes an isometric isomorphism between the spaces of multipolynomials and linear operators. Applications to composition ideals of multipolynomials and to multipolynomials that are of finite rank, approximable, compact, and weakly compact are provided.
G. Botelho, D. Pellegrino, and P. Rueda, On composition ideals of multilinear mappings and homogeneous polynomials, Publ. Res. Inst. Math. Sci. 43 (2007), 1139–1155.MathSciNetCrossRefzbMATHGoogle Scholar
A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam, 1993.zbMATHGoogle Scholar
J. Diestel, H. Jarchow, and A. Pietsch, Operator ideals, In: Handbook of the Geometry of Banach Spaces, Vol. I, 437-496, North-Holland Amsterdam, 2001.CrossRefzbMATHGoogle Scholar
K. Floret, Natural norms on symmetric tensor products of normed spaces, Proceedings of the Second International Workshop on Functional Analysis (Trier, 1997), Note Mat. 17 (1997), 153–188 (1999).Google Scholar