Annals of Functional Analysis

Orthogonal complementing in Hilbert C-modules

Boris Guljaš

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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.

Article information

Ann. Funct. Anal., Volume 10, Number 2 (2019), 196-202.

Received: 3 October 2018
Accepted: 19 October 2018
First available in Project Euclid: 19 March 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46C50: Generalizations of inner products (semi-inner products, partial inner products, etc.)

Hilbert $C^{*}$-modules $C^{*}$-algebra of compact operators orthogonal complements orthogonal closure strict closure


Guljaš, Boris. Orthogonal complementing in Hilbert $C^{*}$ -modules. Ann. Funct. Anal. 10 (2019), no. 2, 196--202. doi:10.1215/20088752-2018-0028.

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