作为K-谱集的黎曼球面多个圆的交
Intersections of several disks of the Riemann sphere as K-spectral sets
摘要：
证明了：若黎曼球面上的$n$闭圆$D_1, D_2, ..., D_n$，是Hilbert空间上有界线性算子$A$的谱集，则它们的交$D_1\cap D_2...\cap D_n$是$A$的完备$K$ -谱集，其中有$K\leq n+n(n-1)/\sqrt3$ .当$n=2$和交点$X_1\cap X_2$是一个环时，这个结果对A. L. Shields（1974）的一个问题给出了肯定的回答。
英文摘要：
We prove that if $n$ closed disks $D_1, D_2, ..., D_n$, of the Riemann sphere are spectral sets for a bounded linear operator $A$ on a Hilbert space, then their intersection $D_1\cap D_2...\cap D_n$ is a complete $K$-spectral set for $A$, with $K\leq n+n(n-1)/\sqrt3$. When $n=2$ and the intersection $X_1\cap X_2$ is an annulus, this result gives a positive answer to a question of A.L. Shields (1974).
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