For a C*-algebra $A$, the cone over $A$ is $CA=C_{0}(0,1]\otimes A$ ,
My question: If $A$ is separable, $CA$ is also separable?
2026-03-30 00:16:47.1774829807
The cone over separable C*-algebra is also separable?
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Yes. The tensor product of separable algebras is separable. You can construct a dense subset of the tensor product by taking the algebraic tensor of two countable dense subsets of each algebra.