论文标题
数值半径和贝雷辛数不等式
Numerical radius and Berezin number inequality
论文作者
论文摘要
我们研究了希尔伯特空间上有界线性算子的数值半径和贝雷唱的各种不平等。事实证明，纯度两等级的数值半径为1，纯度两次分析的crawford数为0。特别是，我们表明，对于任何标量 - valueDnon-contant-contant内部函数$θ$，数值半径，数值radius和crawford的crawford数量a toeplitz ocerator $ t_tion $t_θ$ on a Hardy Space是1和0和0和0和0和0和0和0和0和0。还表明，数值半径是一类异构体的乘法性，对于一类移位的换向物而言是次级的。我们用一些具体的例子说明了这些结果。最后，在经典的Hardy的不平等的帮助下，建立了某些类似某些运营商的Berezin数量的硬质类型的不平等现象。
We study various inequalities for numerical radius and Berezin number of a bounded linear operator on a Hilbert space. It is proved that the numerical radius of a pure two-isometry is 1 and the Crawford number of a pure two-isometry is 0. In particular, we show that for any scalar-valuednon-constant inner function $θ$, the numerical radius and the Crawford number of a Toeplitz operator $T_θ$ on a Hardy space is 1 and 0, respectively. It is also shown that numerical radius is multiplicative for a class of isometries and sub-multiplicative for a class of commutants of a shift. We have illustrated these results with some concrete examples. Finally, some Hardy-type inequalities for Berezin number of certain class of operators are established with the help of the classical Hardy's inequality.
