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.
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