论文标题
$ C^*$ - 代数的$ a $ numerical radius的扩展
An extension of the $a$-numerical radius on $C^*$-algebras
论文作者
论文摘要
让$ a $是Unital $ c^*$ - 代数$ \ mathfrak {a} $中的积极元素。我们在$ \ mathfrak {a} $上定义了半符号，该$ \ a $ a $ a-operator semi-Norm和$ a $ numerical radius。我们研究了该半符号的基本特性，并证明了涉及它的不平等。此外，我们为$ \ mathfrak {a} $中的$ a $ numerical元素提供了新的上限和下限。还讨论了其他一些相关的结果。
Let $a$ be a positive element in a unital $C^*$-algebra $\mathfrak{A}$. We define a semi-norm on $\mathfrak{A}$, which generalizes the $a$-operator semi-norm and the $a$-numerical radius. We investigate basic properties of this semi-norm and prove inequalities involving it. Further, we derive new upper and lower bounds for the $a$-numerical radii of elements in $\mathfrak{A}$. Some other related results are also discussed.
