an:05635969
Zbl 1207.46061
Burgos, Mar??a; Fern??ndez-Polo, Francisco J.; Garc??s, Jorge J.; Peralta, Antonio M.
Orthogonality preservers revisited
EN
Asian-Eur. J. Math. 2, No. 3, 387-405 (2009).
00254228
2009
j
46L70 17C65 47B48 46L05 46L40 46B04
orthogonality preserving operators; orthogonally additive mappings; \(C^*\)-algebras; \(\text{JB}^*\)-algebras; \(\text{JB}^*\)-triples
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: \textit{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; \textit{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 \textit{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.
Antonio Fern??ndez L??pez (Malaga)
Zbl 0488.47016; Zbl 0803.46069; Zbl 1108.46041