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A Revised Formula for a Locally Bounded Pseudocharacter on an Almost Connected Locally Compact Group, Shtern A.Iстатья
- Автор: Штерн А.И.
- Журнал: Advanced Studies in Contemporary Mathematics (Kyungshang)
- Том: 32
- Номер: 4
- Год издания: 2022
- Издательство: Guduk Co.
- Местоположение издательства: Korea, Republic of
- Первая страница: 543
- Последняя страница: 548
- DOI: 10.17777/ascm2022.32.4.543
- Аннотация: As was proved in the paper Shtern A. I., Description of locally boundedpseudocharacters on almost connected locally compact groups, Russ. J. Math.Phys. {\bf23} (2016), no. 4, 551--552, if $G$ is an almost connected locallycompact group and $G_0$ is the connected component of the identity in $G$, thenevery locally bounded pseudocharacter of $G$ is a uniquely defined extension to$G$ of a locally bounded pseudocharacter on $G_0$. We prove here that everylocally bounded pseudocharacter on $G_0$ admits an extension to a uniquelydefined locally bounded pseudocharacter of $G$. Thus, all pseudocharacters on$G$ are in a one-to-one correspondence with the pseudocharacters on $G_0$described in Theorem~1 of the aforementioned paper. We also correct the formulain the paper Shtern A. I., A formula for pseudocharacters on almost connectedgroups, Russ. J. Math. Phys. {\bf25} (2018), no. 4, 531--533, connecting alocally bounded pseudocharacter of $G$ and its restriction to $G_0$.
- Добавил в систему: Штерн Александр Исаакович