ORTHOGONAL COMPLEMENTING IN HILBERT C*-MODULES

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.