Abstract
We introduce the notion of \(*\)-Jordan homomorphism map to obtain a Hua type theorem on alternative \(*\)-algebras endowed with an involution, relating in which conditions a \(*\)-Jordan homomorphism preserves \(*\)-generalized inverses. Even more, we prove that the bijective unital continuous linear maps on octonion algebra \(\mathbb {O}\) whose preserves \(*\)-generalized invertibility are \(*\)-Jordan homomorphism maps.
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The authors would like to thank the referees for the valuable reviews and comments as well as for the helpful suggestions, which helped to improve the work.
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The third author was supported by São Paulo Research Foundation (FAPESP), Brazil under Grant No. 2022/02571-4. The second author was supported by the Centre for Mathematics of the University of Coimbra - UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES.
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The third author was supported by São Paulo Research Foundation (FAPESP), Brazil under grant number 2022/02571-4. The second author was partially supported by the Centre for Mathematics of the University of Coimbra (funded by the Portuguese Government through FCT/MCTES, DOI 10.54499/UIDB/00324/2020).
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Ferreira, B.L.M., Barreiro, E. & de Araujo Smigly, D. A Hua-type theorem for Cayley algebras. Rend. Circ. Mat. Palermo, II. Ser (2024). https://doi.org/10.1007/s12215-024-01029-z
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DOI: https://doi.org/10.1007/s12215-024-01029-z