Complete orthogonality preservers between C${}^{\ast }$-algebras

Abstract

We introduce $n$-orthogonality (and completely orthogonality) preserving operators between C${}^{\ast }$-algebras. Our main theorem states that every completely orthogonality preserving bounded linear mapping between C${}^{\ast }$-algebras is a weighted TRO homomorphism. We also give several characterisations of TRO homomorphisms among triple homomorphisms.

Cited by in corpus (2)

• Automatic continuity of biorthogonality preservers between weakly compact JB${}^{\ast }$-triples and atomic JBW${}^{\ast }$-triples
• Contractive linear preservers of absolutely compatible pairs between C*-algebras