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Extendibility of homogeneous polynomials on Banach spaces. (English) Zbl 0890.46032

Summary: We study the \(n\)-homogeneous polynomials on a Banach space \(X\) that can be extended to any space containing \(X\). We show that there is an upper bound on the norm of the extension. We construct a predual for the space of all extendible \(n\)-homogeneous polynomials on \(X\) and we characterize the extendible 2-homogeneous polynomials on \(X\) when \(X\) is a Hilbert space, an \(\mathcal L_1\)-space or an \(\mathcal L_\infty\)-space.

MSC:

46G20 Infinite-dimensional holomorphy
46B28 Spaces of operators; tensor products; approximation properties
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