论文标题
拓扑半群及其在Ergodic和固定点理论中的应用的弱形式
A Weak Form of Amenability of Topological Semigroups and its Applications in Ergodic and Fixed Point Theories
论文作者
论文摘要
在本文中，我们在拓扑半群上引入了一种薄弱的舒适性，我们称为$φ$ - 毫无用处，其中$φ$是拓扑半群上的角色。获得了这个新概念的一些基本属性，通过举例说明，我们表明该定义比Semigroups的敏感性弱。作为一个值得注意的结果，对于拓扑半群$ s $，可以表明，如果$ s $是$φ$ - ableable，则$ s $是可正常的。此外，引入了拓扑半群$ s $的$φ$ - 果态，并证明在某些条件下，在$ s $和Banach Space $ x $，$φ$ - 不明式和$φ$ ersecodicity的任何反对责任所定义的任何反对责任$ s $ s $ s $上的$ x $等等。研究了$φ$ - 拓扑半群的肯定性与共同固定点的存在之间的关系，通过这种关系，在定义和研究的$φ$ - 不明式的意义上，拓扑半群的Hahn-Banach属性。
In this paper, we introduce a weak form of amenability on topological semigroups that we call $φ$-amenability, where $φ$ is a character on a topological semigroup. Some basic properties of this new notion are obtained and by giving some examples, we show that this definition is weaker than the amenability of semigroups. As a noticeable result, for a topological semigroup $S$, it is shown that if $S$ is $φ$-amenable, then $S$ is amenable. Moreover, $φ$-ergodicity for a topological semigroup $S$ is introduced and it is proved that under some conditions on $S$ and a Banach space $X$, $φ$-amenability and $φ$-ergodicity of any antirepresntation defined by a right action $S$ on $X$, are equivalent. A relation between $φ$-amenability of topological semigroups and existance of a common fixed point is investigated and by this relation, Hahn-Banach property of topological semigroups in the sense of $φ$-amenability defined and studied.
