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In this paper, we introduce a new technique in the study of the *{*}-regular closure of some specific group algebras KG inside 𝒰(G){{\mathcal{U}}(G)}, the *{*}-algebra of unbounded operators affiliated to the group von Neumann algebra 𝒩(G){{\mathcal{N}}(G)}. The main tool we use for this study is a general approximation result for …