论文标题
Banach代数上乘法运算符的弱顺序特性
Weak Sequential Properties of the Multiplication Operators on Banach Algebras
论文作者
论文摘要
让$ a $为Banach代数。对于$ f \在a^{\ ast} $中，我们检查了众所周知的映射$ t_f：a \ to a^{\ ast} $，$ t_f（a）= fa $的弱顺序属性，其中$ fa \ in a^{\ ast} $在$ fa（x）中定义了$ fa（x）= f（ax）$ a $ in $ a $ a $ a $ a $ for a^{\ ast} $。我们提供等同的条件，何时$ t_f $在a^{\ ast} $中的每一个$ f \以及当$ t_f $映射薄弱的预先计算集合到a^{\ ast} $中的每个$ f \时。我们的结果在Banach Space $ x $上的紧凑型操作员$ k（x）$的代数申请。
Let $A$ be a Banach algebra. For $f\in A^{\ast}$, we inspect the weak sequential properties of the well-known map $T_f:A\to A^{\ast}$, $T_f(a) = fa$, where $fa\in A^{\ast}$ is defined by $fa(x) = f(ax)$ for all $x\in A$. We provide equivalent conditions for when $T_f$ is completely continuous for every $f\in A^{\ast}$, and for when $T_f$ maps weakly precompact sets onto L-sets for every $f\in A^{\ast}$. Our results have applications to the algebra of compact operators $K(X)$ on a Banach space $X$.
