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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: {\it 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; {\it 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 {\it N.-C.\thinspace 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.

46L70Nonassociative selfadjoint operator algebras
17C65Jordan structures on Banach spaces and algebras
47B48Operators on Banach algebras
46L05General theory of $C^*$-algebras
46L40Automorphisms of $C^*$-algebras
46B04Isometric theory of Banach spaces
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