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Orthogonality preservers revisited. (English) Zbl 1207.46061
The authors obtain a complete characterization of all orthogonality preserving operators from a \(\text{JB}^*\)-algebra to a \(\text{JB}^*\)-triple by using techniques which mainly come from \(\text{JB}^*\)-triple theory and which are independent of the results previously obtained by other authors dealing with this subject: W. Arendt [Indiana Univ. Math. J. 32, 199–215 (1983; Zbl 0488.47016)] who initiated the study by considering operators preserving disjoint continuous complex functions of a compact space; M. Wolff [Arch. Math. 62, No. 3, 248–253 (1994; Zbl 0803.46069)] who established a full description of the symmetrical orthogonality preserving bounded linear operators \(T: A\to B\) between \(C^*\)-algebras with \(A\) being unital; and N.-C. Wong [Southeast Asian Bull. Math. 29, No. 2, 401–407 (2005; Zbl 1108.46041)] who showed that \(T: A\to B\) is a triple homomorphism if and only if it is orthogonality preserving and \(T^{**}(1)\) is a partial isometry (tripotent), thus expressing the problem in \(\text{JB}^*\)-triple terms.

MSC:
46L70 Nonassociative selfadjoint operator algebras
17C65 Jordan structures on Banach spaces and algebras
47B48 Linear operators on Banach algebras
46L05 General theory of \(C^*\)-algebras
46L40 Automorphisms of selfadjoint operator algebras
46B04 Isometric theory of Banach spaces
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