Abstract

The author in [30] obtain a complete characterization of all orthogonality preserving operators from a JB*-algebra to a π½π΅βˆ—-triple following [30]. If π‘‡π‘šβˆΆ 𝐽 β†’ 𝐸 is a bounded linear operator from a π½π΅βˆ—-algebra (respectively, a πΆβˆ—-algebra) to a π½π΅βˆ—-triple and β„Žπ‘š denotes the element π‘‡π‘šβˆ—βˆ—(1), then π‘‡π‘š is orthogonality preserving, if and only if, π‘‡π‘š preserves zero-triple-products, if and only if, there exists a Jordan βˆ—-homomorphism π‘†π‘šβˆΆ 𝐽 β†’ 𝐸2βˆ—βˆ—(π‘Ÿ(β„Žπ‘š)) such that π‘†π‘š(π‘₯) and β„Žπ‘š operator commute and π‘‡π‘š(π‘₯)= β„Žπ‘šβ€’π‘Ÿ(β„Žπ‘š)π‘†π‘š(π‘₯), for every π‘₯ ∈ 𝐽, where π‘Ÿ(β„Žπ‘š) is the range tripotent of β„Žπ‘š,𝐸2βˆ—βˆ—(π‘Ÿ(β„Žπ‘š)) is the Peirce-2 subspace associated to π‘Ÿ(β„Žπ‘š) and β€’π‘Ÿ(β„Žπ‘š) is the natural product making 𝐸2βˆ—βˆ—(π‘Ÿ(β„Žπ‘š)) a π½π΅βˆ—-algebra. This characterization culminates the description of all orthogonality preserving operators between πΆβˆ—-algebras and π½π΅βˆ—-algebras and show a widegeneralizations.

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