论文标题
$ a $ a-numerical半径不平等的不平等现象的改善
Improvement of $A$-numerical radius inequalities of semi-Hilbertian space operators
论文作者
论文摘要
令$ \ mathcal {h} $为复杂的希尔伯特空间，让$ a $为$ \ MATHCAL {H} $的正运算符。我们获得了$ a $ numerical radius在半希尔伯特空间中的运算符$ \ Mathcal {b} _a（\ Mathcal {h}）$中的新界限，这些范围概括并改善了现有的$。此外，我们估计了$ b $ - 操作器seminorm和$ b $ numerical半径为$ 2 \ times 2 $ 2 $运算符矩阵，其中$ b = \ mbox {diag}（a，a，a）$。此处获得的界限改进了现有的界限。
Let $\mathcal{H}$ be a complex Hilbert space and let $A$ be a positive operator on $\mathcal{H}$. We obtain new bounds for the $A$-numerical radius of operators in semi-Hilbertian space $\mathcal{B}_A(\mathcal{H})$ that generalize and improve on the existing ones. Further, we estimate bounds for the $B$-operator seminorm and $B$-numerical radius of $2\times 2$ operator matrices, where $B=\mbox{diag}(A,A)$. The bounds obtained here improve on the existing ones.
