Nuclear C*-algebra

In mathematics, a nuclear C*-algebra is a C*-algebra A such that the injective and projective C*-cross norms on A⊗B are the same for every C*-algebra B. These were first studied by Takesaki (1964) under the name "Property T" (this is unconnected with Kazhdan's property T). Equivalently, a C*-algebra is nuclear if the identity map, as a completely positive map, approximately factors through matrix algebras. One might say that these are C*-algebras that admit noncommutative "partitions of unity."

A C*-algebra is nuclear if and only if its enveloping von Neumann algebra is injective.

See also

• Nuclear space

References

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