Supplement to ''Hodge spectral sequence on compact Kähler spaces'' (Q1190736)

The purpose of this short note is to supplement the author's previous article [Publ. Res. Inst. Math. Sci. 23, 613-625 (1987; Zbl 0635.32008)] by exhibiting a rigorous proof of the dual \(L^ 2\) Poincaré lemma as well as its \(\overline\partial\)-analogue (cf. Proposition 4.1 (7), p. 272 in the cited paper). We have stated there that up to a slight change its proof is similar to that of the ordinary one, for which we had given a detailed proof. However, it turned out that the proof requires a different technique which does not seem to be in the literature. Therefore the author would like to present it here.