论文标题
Banach Space $ c（k）$阅读$ k $的尺寸
A Banach space $C(K)$ reading the dimension of $K$
论文作者
论文摘要
假设詹森的钻石原理（$ \ diamondsuit $）我们为每个自然数字$ n> 0 $构建，那么每当Banach Space $ c（k）$ c（k）$和$ c（l）$紧凑的Hausdorff space $ k $，对于某些紧凑型Hausdorff $ l $的封面上的$ l $等于$ n $。构造的空间$ k $是可分开的，并且Banach Space $ c（k）$几乎没有运营商，即每个有界的线性运算符$ t：c（k）\ rightarrow c（k）$属于$ t（f）= fg+s（f）的形式，而在$ g \ in c（k）$ in c（k）$和$ s $ ables $ s $。
Assuming Jensen's diamond principle ($\diamondsuit$) we construct for every natural number $n>0$ a compact Hausdorff space $K$ such that whenever the Banach spaces $C(K)$ and $C(L)$ are isomorphic for some compact Hausdorff $L$, then the covering dimension of $L$ is equal to $n$. The constructed space $K$ is separable and connected, and the Banach space $C(K)$ has few operators i.e. every bounded linear operator $T:C(K)\rightarrow C(K)$ is of the form $T(f)=fg+S(f)$, where $g\in C(K)$ and $S$ is weakly compact.
