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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 ${T}^{**}\left(1\right)$ 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 Operators on Banach algebras 46L05 General theory of ${C}^{*}$-algebras 46L40 Automorphisms of ${C}^{*}$-algebras 46B04 Isometric theory of Banach spaces