Additivity of Quadratic Maps on JB Algebras
- Авторлар: Hamhalter J.1, Turilova E.2
-
Мекемелер:
- Faculty of Electrical Engineering, Department of Mathematics
- Lobachevskii Institute of Mathematics and Mechanics
- Шығарылым: Том 40, № 10 (2019)
- Беттер: 1483-1488
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205662
- DOI: https://doi.org/10.1134/S1995080219100123
- ID: 205662
Дәйексөз келтіру
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.
Негізгі сөздер
Авторлар туралы
Jan Hamhalter
Faculty of Electrical Engineering, Department of Mathematics
Хат алмасуға жауапты Автор.
Email: hamhalte@math.feld.cvut.cz
Чехия, Prague 6, 166 27
Ekaterina Turilova
Lobachevskii Institute of Mathematics and Mechanics
Хат алмасуға жауапты Автор.
Email: Ekaterina.Turilova@kpfu.ru
Ресей, Kazan, 420008