论文标题
关于在规范空间上连续函数近似的注释
A note on approximation of continuous functions on normed spaces
论文作者
论文摘要
让$ x $成为一个真正可分开的规范空间$ x $承认分离多项式。我们证明，从子集$ a $ x $到真正的Banach空间的每个连续功能可以通过限制到$ a $ a $ a的$ x $的开放子集进行分析。另外，我们还证明，每个连续的功能都可以从一个复杂的可分开的范数空间到复杂的Banach空间，该空间承认分离$*$ - 多项式可以通过$*$ - 分析功能统一地近似。
Let $X$ be a real separable normed space $X$ admitting a separating polynomial. We prove that each continuous function from a subset $A$ of $X$ to a real Banach space can be uniformly approximated by restrictions to $A$ of functions which are analytic on open subsets of $X$. Also we prove that each continuous function to a complex Banach space from a complex separable normed space admitting a separating $*$-polynomial can be uniformly approximated by $*$-analytic functions.
