Nuclear C*-algebra

In the mathematical field of functional analysis, a nuclear C*-algebra is a C*-algebra A such that for every C*-algebra B the injective and projective C*-cross norms coincides on the algebraic tensor product A⊗B and the completion of A⊗B with respect to this norm is a C*-algebra.This property was first studied by Takesaki (1964) under the name "Property T", which is not related to Kazhdan's property T. Nuclearity admits the following equivalent characterizations: The commutative unital C* algebra of (real or complex-valued) continuous functions on a compact Hausdorff space as well as the noncommutative unital algebra of n×n real or complex matrices are nuclear.[1]

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