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Weakly compact multilinear mappings. (English) Zbl 0901.46038

Summary: The notion of Arens regularity of a bilinear form on a Banach space \(E\) is extended to continuous \(m\)-linear forms, in such a way that the natural associated linear mappings, \(E\to{\mathcal L}({}^{m-1}E)\) and \((m-1)\)-linear mappings \(E\times \dots\times E\to E'\), are all weakly compact. Among other applications, polynomials whose first derivative is weakly compact are characterized.

MSC:

46G20 Infinite-dimensional holomorphy
46B20 Geometry and structure of normed linear spaces
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