Boris Guljaš. Source: Annals of Functional Analysis, Volume 10, Number 2, 196--202.Abstract:
We characterize orthogonally complemented submodules in Hilbert $C^{*}$ -modules by their orthogonal closures. Applying Magajna’s characterization of Hilbert $C^{*}$ -modules over $C^{*}$ -algebras of compact operators by the complementing property of submodules, we give an elementary proof of Schweizer’s characterization of Hilbert $C^{*}$ -modules over $C^{*}$ -algebras of compact operators. Also, we prove analogous characterization theorems for $C^{*}$ -algebras of compact operators related to topological properties of submodules of strict completions of Hilbert modules over a nonunital $C^{*}$ -algebra.