论文标题
一些$ \ mathbb {a} $ - $ d \ times d $ operator矩阵的数值半径不平等
Some $\mathbb{A}$-numerical radius inequalities for $d\times d$ operator matrices
论文作者
论文摘要
令$ a $为积极的（半限制）有限的线性运算符，作用于复杂的Hilbert Space $ \ big（\ Mathcal {h}，\ langle \ cdot \ cdot \ cdot \ cdot \ cdot \ rangle \ big）$。半inner产品$ {\ langle x \ mid y \ rangle} _a：= \ langle ax \ mid y \ rangle $，$ x，y \ in \ mathcal {h h} $诱导eminorm $ {\ | \ cdot \ | \ cdot \ |} _a $ on $ n $ \ nmathcal of seminorm $ {令$ t $为$ \ natercal {h} $上的$ a $ and-bound运算符，$ a $ a-numerical radius的$ t $ of $ t $由\ begin {align*}ω___________________________________________________________________________________部门（t）= \ sup \ big \ big \ big \ big | \ Mathcal {h}，\，{\ | x \ |} _a = 1 \ big \}。 \ end {align*}在本文中，我们为$ω__\ mathbb {a}（\ Mathbb {t}）$建立了几个不等式，其中$ \ mathbb {t} =（t_ {ij {ij}）$是$ d \ times d \ times d \ times d \ times d $ d $ operrix with $ t_ $ t_ $ a $ a $ a $ a $ a a $ a a $ a $ \ mathbb {a} $是对角线运算符矩阵，其每个对角线条目为$ a $。
Let $A$ be a positive (semidefinite) bounded linear operator acting on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$. The semi-inner product ${\langle x\mid y\rangle}_A := \langle Ax\mid y\rangle$, $x, y\in\mathcal{H}$ induces a seminorm ${\|\cdot\|}_A$ on $\mathcal{H}$. Let $T$ be an $A$-bounded operator on $\mathcal{H}$, the $A$-numerical radius of $T$ is given by \begin{align*} ω_A(T) = \sup\Big\{\big|{\langle Tx\mid x\rangle}_A\big|: \,\,x\in \mathcal{H}, \,{\|x\|}_A = 1\Big\}. \end{align*} In this paper, we establish several inequalities for $ω_\mathbb{A}(\mathbb{T})$, where $\mathbb{T}=(T_{ij})$ is a $d\times d$ operator matrix with $T_{ij}$ are $A$-bounded operators and $\mathbb{A}$ is the diagonal operator matrix whose each diagonal entry is $A$.
