Семинары: М. Э. Нуриллаев, Nuclear and injective real $C^\ast$-algebras

СЕМИНАРЫ


Функциональный анализ и его приложения 11 октября 2018 г. 10:30, г. Ташкент, Национальный университет Узбекистана, Математический факультет, аудитория А-304, ул. Университетская, 4

Nuclear and injective real $C^\ast$-algebras М. Э. Нуриллаев Ташкентский государственный педагогический университет им. Низами
Аннотация: Nuclear real $C^\ast$-algebras will be considered. It is shown that a real $C^\ast$-algebra is nuclear if and only if its enveloping $C^\ast$-algebra is nuclear. It is proven that a real $C^\ast$-algebra $R$ is nuclear iff the real $W^\ast$-algebra $R^{\ast\ast}$ is injective, where $R^{\ast\ast}$ is the second dual space of $R$. It is proven that a real $W^\ast$-subalgebra $Q$ of a real $W^\ast$-algebra $R$ is maximal injective in $R$ if and only if its enveloping $W^\ast$-algebra $Q + i Q$ is maximal injective in $R + i R$. Moreover, the question is studied: Let $Q_i \subset R_i$ be real $W^\ast$-algebras $(i=1,2)$. If $Q_i$ is a maximal injective real $W^\ast$-subalgebra $(i=1,2)$, then is $Q_1 \otimes Q_2$ maximal injective in $R_1 \otimes R_2$? Positive answer is done for some particular cases.