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4. Nuclearity


    1. Add remark

      Problem 4.1.

      Is every stably finite nuclear separable C*-algebra locally approximable by type I C*-algebras?

        •     All presently known nuclear C*-algebras are obtained from $\mathbb C$ by taking closure under simple operations such as tensoring with finite-dimensional matrix algebras and taking inductive limits. They belong to the so-called bootstrap class.

          Add remark

          Problem 4.2.

          Does every nuclear C*-algebra belong to the bootstrap class?


            • Add remark

              Problem 4.3.

              Do all nuclear C*-algebras satisfy the UCT (Universal Coefficient Theorem)?

                  Cite this as: AimPL: Set theory and C* algebras, available at http://aimpl.org/settheorycstar.