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| ON THE JOINT SPECTRUM FOR N-TUPLE OF HYPONORMAL OPERATORS |
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Citation： |
Zhang Dianzhou,Huang Danrun.ON THE JOINT SPECTRUM FOR N-TUPLE OF HYPONORMAL OPERATORS[J].Chinese Annals of Mathematics B,1986,7(1):14~23 |
| Page view： 900
Net amount： 1029 |
Authors： |
Zhang Dianzhou; Huang Danrun |
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| 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
$\[\left\| A \right\| = {r_{zp}}(A)\]$ |
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