Topological properties of spaces of ideals of the minimal tensor product

Details Topological properties of spaces of ideals of the minimal tensor product Topological properties of spaces of ideals of the minimal tensor product

2009-06-16

arxiv.org/abs/0906.2896v1

Mathematics

Operator Algebras

7 pages

Scientific paper

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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