The \(\overline{\partial}\) problem for \((0,2)\)-forms in infinite dimensional complex spaces
Let \(E\) be a nuclear DF space and \(\Omega \) a pseudoconvex domain in \(E\). Let \(f:\Omega \rightarrow \Lambda^{(0,2)}(E)\) be a holomorphic \((0,2)\)-form. It is shown that there exists a \(\mathcal C^{\infty }\) \((0,1)\)-form \(g\) on \(\Omega \) such that \(\overline \partial g = f.\) For the proof of this result the authors use a corresponding result on separable Hilbert spaces and a certain approximation theorem for holomorphic functions on Hilbert spaces.
scientific article; zbMATH DE number 1335031