满足Shapiro定理的逼近格式的特征
Characterization of approximation schemes satisfying Shapiro's Theorem
摘要：
在本文中，我们描述的逼近方案，满足Shapiro定理，我们使用这个结果的几个经典的逼近过程。特别是，我们研究了有限秩算子的逼近和几个字典和规范的n项逼近。此外，我们还将我们的主要定理与俞敏洪的一个经典结果进行了比较。Brundyi和我们展示了两个不满足Shapiro定理的近似方案的例子。
英文摘要：
In this paper we characterize the approximation schemes that satisfy Shapiro's theorem and we use this result for several classical approximation processes. In particular, we study approximation of operators by finite rank operators and n-term approximation for several dictionaries and norms. Moreover, we compare our main theorem with a classical result by Yu. Brundyi and we show two examples of approximation schemes that do not satisfy Shapiro's theorem.
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