| ON THE JOINT SPECTRUM FOR N-TUPLE OF HYPONORMAL OPERATORS |
| |
| 作者姓名： | Zhang Dianzhou Huang Danrun |
| |
| 作者单位： | Department of Mathematics East China Normal University，Shanghai，China.，Department of Mathematics，East China Normal University，Shanghai，China. |
| |
| 摘 要： | Let A=(A_1,…,A,)be an n-tuple of double commuting hyponormal operators.It is-proved that:1.The joint spectrum of A has a Cartesian decomposition:ReSp(A)]=S_p(ReA),ImSp(A)]=Sp(ImA);2.The.joint resolvent of A satisfies the growth condition:‖()‖=1/(dist(z,Sp(A)));3.If 0σ(A_i),i=1,2,…,n,then‖A‖=γ_(sp)(A).
|
| 收稿时间： | 1983/12/27 0:00:00 |
ON THE JOINT SPECTRUM FOR N-TUPLE OF HYPONORMAL OPERATORS |
| |
| Zhang Dianzhou,Huang Danrun.ON THE JOINT SPECTRUM FOR N-TUPLE OF HYPONORMAL OPERATORS[J].Chinese Annals of Mathematics,Series B,1986,7(1):14-23. |
| |
| Authors: | Zhang Dianzhou and Huang Danrun |
| |
| Institution: | Department of Mathematics, East China Normal University, Shanghai, China. |
| |
| Abstract: | Let $\A = ({A_1}, \cdots ,{A_n})\]$ be an n-tuple of double commuting hyponormal operators. It is proved that: 1. The joint spectrum of A has a Cartesian decomposition;
$\{\mathop{\rm Re}\nolimits} Sp(A)] = {S_p}({\mathop{\rm Re}\nolimits} A),{\mathop{\rm Im}\nolimits} Sp(A)] = {S_p}({\mathop{\rm Im}\nolimits} A)\]$; 2. The joint resolvent of A satisfies the growth eondition:
$\\left\| {(\widehat {A - z})} \right\| = \frac{1}{{dist(z,{S_p}(A))}}\]$;
3. If $\0 \notin \sigma ({A_i}),i = 1, \cdots ,n\]$ then
$\\left\| A \right\| = {r_{zp}}(A)\]$ |
| |
| Keywords: | |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《数学年刊B辑(英文版)》浏览原始摘要信息 |
| 点击此处可从《数学年刊B辑(英文版)》下载免费的PDF全文 |
|
