Shanshan Hua

Approximations and classification program for C*-algebras

One of the central notions in the study of C*-algebras is nuclearity, which can be viewed as an internal finite-dimensional approximation property. Nuclear C*-algebras include a broad class of examples; for instance, the group C*-algebras of amenable groups are nuclear. In this talk, we present an equivalent characterization of nuclearity in terms of pure states on C*-algebras. This perspective is both natural and insightful—for example, in the commutative case, applying a partition of unity leads directly to this property. Beyond its intrinsic interest, this characterization has further applications in understanding regularity properties of maps between C*-algebras. In particular, we establish more general criteria under which a map, in a suitable sense, absorbs the Jiang-Su algebra—a recurring and significant feature in the Elliott classification program for C*-algebras.