Prieto, Ángeles The bidual of spaces of holomorphic functions in infinitely many variables. (English) Zbl 0741.46016 Proc. R. Ir. Acad., Sect. A 92, No. 1, 1-8 (1992). 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) Cited in 2 Documents 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)) Keywords:holomorphic functions of bounded type; bidual spaces; Schauder decompositions PDFBibTeX XMLCite \textit{Á. Prieto}, Proc. R. Ir. Acad., Sect. A 92, No. 1, 1--8 (1992; Zbl 0741.46016)