Additivity of Quadratic Maps on JB Algebras
- Авторы: Hamhalter J.1, Turilova E.2
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Учреждения:
- Faculty of Electrical Engineering, Department of Mathematics
- Lobachevskii Institute of Mathematics and Mechanics
- Выпуск: Том 40, № 10 (2019)
- Страницы: 1483-1488
- Раздел: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205662
- DOI: https://doi.org/10.1134/S1995080219100123
- ID: 205662
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Аннотация
The problem of automatic additivity of Jordan type homomorphisms has received a great deal of attention in theory of operator algebras as well in ring theory. We study additivity of quadratic maps, that is the maps between Jordan Banach algebras that preserve the quadratic product (a, b) → aba. The main result shows that any continuous quadratic bijective map between unital Jordan Banach algebras that is linear on associative subalgebras is automatically additive. This contributes to the Borification program in quantum theory and Mackey-Gleason problem on linearity of quasi-linear maps.
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Об авторах
Jan Hamhalter
Faculty of Electrical Engineering, Department of Mathematics
Автор, ответственный за переписку.
Email: hamhalte@math.feld.cvut.cz
Чехия, Prague 6, 166 27
Ekaterina Turilova
Lobachevskii Institute of Mathematics and Mechanics
Автор, ответственный за переписку.
Email: Ekaterina.Turilova@kpfu.ru
Россия, Kazan, 420008