论文标题
大约$ a $ spectral半径不平等，$ a $ a的希尔伯特太空运营商
Some $A$-spectral radius inequalities for $A$-bounded Hilbert space operators
论文作者
论文摘要
令$ r_a（t）$表示运算符$ t $的$ a $ a-spectral半径，该半径相对于复杂的Hilbert Space $ \ Mathcal {H h} $在正面操作员$ a $引起的eminorm界定。在本文中，我们旨在建立一些$ a $ a $ and-and-and-and-and-and-and-and-and-and-and-and-and-and-and-and-and-and-and-and-and-and-and-collinganters的不平等现象。此外，在适当的条件下，$ t $和$ a $我们表明 \ begin {equination*} r_a \ left（\ sum_ {k = 0}^{+\ iftty} c_ {k} t^{k} \ right）\ leq \ sum_ {k = 0} \ end {equation*}其中$ c_k $都是\ mathbb {n} $的所有$ k \的复数数字。
Let $r_A(T)$ denote the $A$-spectral radius of an operator $T$ which is bounded with respect to the seminorm induced by a positive operator $A$ on a complex Hilbert space $\mathcal{H}$. In this paper, we aim to establish some $A$-spectral radius inequalities for products, sums and commutators of $A$-bounded operators. Moreover, under suitable conditions on $T$ and $A$ we show that \begin{equation*} r_A\left( \sum_{k=0}^{+\infty}c_{k}T^{k}\right) \leq \sum_{k=0}^{+\infty}|c_{k}|\left[r_A(T)\right]^{k}, \end{equation*} where $c_k$ are complex numbers for all $k\in \mathbb{N}$.
