极小张量积理想空间的拓扑性质
Topological properties of spaces of ideals of the minimal tensor product
摘要：
证明了对于两个C^*-代数A_1和A_2，Prim（A_1）\times Prim（A_2）上的任意连续函数只要取值于T_1拓扑空间，就可以连续扩张到Prim（A_1 \otimes A_2）.这推广了L.G.布朗对R. J. Archbold关于A_1 \otimes A_2的极小原理想空间的一个结果给出了新的证明.为了得到这两个结果之一，利用了最小张量积的素理想空间的拓扑性质。
英文摘要：
One shows that for two C^*-algebras A_1 and A_2 any continuous function on Prim(A_1)\times Prim(A_2) can be continuously extended to Prim(A_1\otimes A_2) provided it takes its values in a T_1 topological space. This generalizes a 1977 result of L.G. Brown. A new proof is given for a result of R.J. Archbold about the space of minimal primal ideals of A_1\otimes A_2. To obtain these two results one makes use of the topological properties of the space of prime ideals of the minimal tensor product.
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