Existence of the Solutions of the Cauchy-Riemann Equations

We show that the Cauchy-Riemann equations for holomorphic (0, 2)-forms on Hilbert spaces is solvable on a pseudoconvex open subset. By using this result, we investigate the existence of the solution of the Cauchy-Riemann equation for holomorphic (0, 2)-forms on a pseudoconvex domain in D.F.N. spaces.