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

izvorni znanstveni rad

izvorni znanstveni rad

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

Vrsta prilog u časopisu
Tip izvorni znanstveni rad
Godina 2016
Časopis Annals of functional analysis
Nadređena publikacija Annals of functional analysis
Volumen 7
Svesčić 1
Stranice str. 17-23
DOI 10.1215/20088752-3158195
ISSN 2639-7390
EISSN 2008-8752
Status objavljeno

Sažetak

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.

Ključne riječi

Hilbert C*-modules ; inner product orthogonality ; Birkhoff-James orthogonality ; strong Birkhoff-James orthogonality ; symmetry