论文标题
连续功能的规范空间的乘数代数
Multiplier algebras of normed spaces of continuous functions
论文作者
论文摘要
在本文中，我们研究了连续函数（NSCF）的规范空间的乘数代数的一些一般属性。特别是，我们证明乘数代数继承了NSCF的某些属性。我们表明，通常可以构建仅接收恒定乘数的NSCF。为了做到这一点，使用[23]中的方法，我们证明可以在任何可分开的Metrizable空间上实现任何可分离的Banach空间。另一方面，我们为乘数代数的不可分割性提供了足够的条件。
In this article we investigate some general properties of the multiplier algebras of normed spaces of continuous functions (NSCF). In particular, we prove that the multiplier algebra inherits some of the properties of the NSCF. We show that it is often possible to construct NSCF's which only admit constant multipliers. In order to do that, using a method from [23], we prove that any separable Banach space can be realized as a NSCF over any separable metrizable space. On the other hand, we give a sufficient condition for non-separability of a multiplier algebra.
