Extending Polynomials in Maximal and Minimal Ideals
Copyright policy )Extending Polynomials in Maximal and Minimal Ideals
Given a homogeneous polynomial on a Banach space E belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of E and prove that this extension remains in the ideal and has the same ideal norm. As a consequence, we show that the Aron–Berner extension is a well defined isometry for any maximal or minimal ideal of homogeneous polynomials. This allows us to obtain symmetric versions of some basic results of the metric theory of tensor products.
- University of Buenos Aires Argentina
- National Scientific and Technical Research Council Argentina
maximal ideals, polynomial ideals, SYMMETRIC TENSOR PRODUCTS OF BANACH SPACES, Polynomial ideals, Functional Analysis (math.FA), POLYNOMIAL IDEALS, Aron-Berner extension, Mathematics - Functional Analysis, EXTENSION OF POLYNOMIALS, minimal ideals, Ideals of polynomials and of multilinear mappings in operator theory, (Spaces of) multilinear mappings, polynomials, FOS: Mathematics, https://purl.org/becyt/ford/1.1, 46G25, 46A32, 46B28, 47H60, symmetric tensor products of Banach spaces, Extension of polynomials, Symmetric tensor products of banach spaces, https://purl.org/becyt/ford/1, Spaces of operators; tensor products; approximation properties
maximal ideals, polynomial ideals, SYMMETRIC TENSOR PRODUCTS OF BANACH SPACES, Polynomial ideals, Functional Analysis (math.FA), POLYNOMIAL IDEALS, Aron-Berner extension, Mathematics - Functional Analysis, EXTENSION OF POLYNOMIALS, minimal ideals, Ideals of polynomials and of multilinear mappings in operator theory, (Spaces of) multilinear mappings, polynomials, FOS: Mathematics, https://purl.org/becyt/ford/1.1, 46G25, 46A32, 46B28, 47H60, symmetric tensor products of Banach spaces, Extension of polynomials, Symmetric tensor products of banach spaces, https://purl.org/becyt/ford/1, Spaces of operators; tensor products; approximation properties
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