论文标题
BANACH全态函数空间中的线性多项式近似方案
Linear polynomial approximation schemes in Banach holomorphic function spaces
论文作者
论文摘要
令$ x $为单元磁盘上的Banach Holomorthic功能空间。 $ x $的线性多项式近似方案是一系列有界线性运算符$ t_n：x \ to x $，属性，对于每个$ f \ in x $中的每个$ f \，函数$ t_n（f）$是多项式融合到空间规范的$ f $。我们完全表征那些接收线性多项式近似方案的$ x $。特别是，我们表明，$ x $中的多项式密度不够。
Let $X$ be a Banach holomorphic function space on the unit disk. A linear polynomial approximation scheme for $X$ is a sequence of bounded linear operators $T_n:X\to X$ with the property that, for each $f\in X$, the functions $T_n(f)$ are polynomials converging to $f$ in the norm of the space. We completely characterize those spaces $X$ that admit a linear polynomial approximation scheme. In particular, we show that it is NOT sufficient merely that polynomials be dense in $X$.
