论文标题
$ \ mathbb {a} $ - 某些$ 2 \ times 2 $运算符矩阵的数字半径
Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices
论文作者
论文摘要
对于一个复杂的Hilbert Space $ \ big（\ Mathcal {h}，\ langle \ cdot \ cdot \ mid \ cdot \ cdot \ rangle \ big）$，对于给定有界有界的正线性运算符$ a $ \ cdot \ rangle_a \ big）$其中$ {\ langle x \ mid y \ rangle} _a：= \ langle ax \ mid y \ y \ rangle $，每$ x，y \ in \ mathcal {h mathcal {h} $。 $ a $ a $ a $ a $ a $ a的$ numerical半径$ \ nathcal {h} $在\ begin {align*}ω_a（t）= \ sup \ sup \ big \ {\ big | {\ big | { \，\，x \ in \ Mathcal {h}，\，{\ langle x \ mid x \ rangle} _a = 1 \ big \}。 \ end {align*}我们在本文中的目的是推导几个$ \ mathbb {a} $ - 数值半径不等式的$ 2 \ times 2 $ 2 $操作员矩阵，其条目为$ a $ bound的操作员，其中$ \ mathbb {a} = a} = \ text = \ diag {diag {diag} {diag}（a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a）$。
For a given bounded positive (semidefinite) linear operator $A$ on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$, we consider the semi-Hilbertian space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle_A \big)$ where ${\langle x\mid y\rangle}_A := \langle Ax\mid y\rangle$ for every $x, y\in\mathcal{H}$. The $A$-numerical radius of an $A$-bounded operator $T$ on $\mathcal{H}$ is given by \begin{align*} ω_A(T) = \sup\Big\{\big|{\langle Tx\mid x\rangle}_A\big|\,; \,\,x\in \mathcal{H}, \,{\langle x\mid x\rangle}_A= 1\Big\}. \end{align*} Our aim in this paper is to derive several $\mathbb{A}$-numerical radius inequalities for $2\times 2$ operator matrices whose entries are $A$-bounded operators, where $\mathbb{A}=\text{diag}(A,A)$.
