一类赋范代数的强零星定理
The Strong Nullstellensatz for Certain Normed Algebras
摘要：
考虑复数上任意有限个变元的多项式环，赋予其系数系$\ell_1$ -范数。它的完备化是绝对收敛于闭多圆盘上的幂级数的巴拿赫代数。而强Hilbert零stellenstructures一般不适用于巴拿赫代数，我们表明，它适用于理想的多项式环是封闭的所示的规范。因此，相应的陈述至少部分地适用于相关的巴拿赫代数。我们还描述了封闭的理想在小的情况下。
英文摘要：
Consider the polynomial ring in any finite number of variables over the complex numbers, endowed with the $\ell_1$-norm on the system of coefficients. Its completion is the Banach algebra of power series that converge absolutely on the closed polydisc. Whereas the strong Hilbert Nullstellensatz does not hold for Banach algebras in general, we show that it holds for ideals in the polynomial ring that are closed for the indicated norm. Thus the corresponding statement holds at least partially for the associated Banach algebra. We also describe the closure of an ideal in small cases.
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