Annals of Functional Analysis

On symmetry of the (strong) Birkhoff–James orthogonality in Hilbert C-modules

Ljiljana Arambašić and Rajna Rajić

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In this note, we prove that the Birkhoff–James orthogonality, as well as the strong Birkhoff–James orthogonality, is a symmetric relation in a full Hilbert A-module V if and only if at least one of the underlying C-algebras A or K(V) is isomorphic to C.

Article information

Ann. Funct. Anal., Volume 7, Number 1 (2016), 17-23.

Received: 2 December 2014
Accepted: 16 February 2015
First available in Project Euclid: 15 October 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L08: $C^*$-modules
Secondary: 46L05: General theory of $C^*$-algebras 46B20: Geometry and structure of normed linear spaces

Hilbert $C^{*}$-modules inner product orthogonality Birkhoff–James orthogonality strong Birkhoff–James orthogonality symmetry


Arambašić, Ljiljana; Rajić, Rajna. On symmetry of the (strong) Birkhoff–James orthogonality in Hilbert $C^{*}$ -modules. Ann. Funct. Anal. 7 (2016), no. 1, 17--23. doi:10.1215/20088752-3158195.

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