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The bidual of spaces of holomorphic functions in infinitely many variables. (English) Zbl 0741.46016

Let \(E\) be an infinite dimensional complex Banach space. Let \({\mathcal H}_ b(E)\) (respectively \({\mathcal H}_{wu}(E)\)) be the space of entire complex valued functions on \(E\) which are bounded (respectively weakly uniformly continuous) when restricted to any bounded subset of \(E\). We obtain Schauder decompositions for \(({\mathcal H}_ b(E),\tau_ b)\) and \(({\mathcal H}_{wu}(E),\tau_ b)\) and we characterise when \({\mathcal H}_ b(E)\) is the bidual of \({\mathcal H}_{wu}(E)\).
Reviewer: Á.Prieto (Madrid)

MSC:

46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
46G20 Infinite-dimensional holomorphy
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
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