论文标题
产品和半希尔伯特太空运营商总和的数值半径不平等
Numerical radius inequalities for products and sums of semi-Hilbertian space operators
论文作者
论文摘要
建立了$ a $ numerical radius产品的新不平等，以及在半希尔伯特空间上作用的运营商总和，即建立了由积极的半决赛操作员$ a $产生的空间。特别是，它适用于运营商$ t $和$ s，$ a $ a-adjoint，$$ω_a（ts）\ leq \ frac {1} {2}ω_a（st）+\ frac {1} {4} {4} \ big（\ | | t \ | _a \ | s \ | s \ | _a+| _a+\ | ts \ | ts \ | _aa \ big） $ a $ a运算符$ t $的经营者。
New inequalities for the $A$-numerical radius of the products and sums of operators acting on a semi-Hilbert space, i.e. a space generated by a positive semidefinite operator $A$, are established. In particular, it is proved for operators $T$ and $S,$ having $A$-adjoint, that $$ ω_A(TS) \leq \frac{1}{2}ω_A(ST)+\frac{1}{4}\Big(\|T\|_A\|S\|_A+\|TS\|_A\Big),$$ where $ω_A(T)$ and $\|T\|_A$ denote the $A$-numerical radius and the $A$-operator seminorm of an operator $T$.
