A separable -algebra is a C*-algebra whose underlying Banach space is a separable topological space.
Chun-Yen Chou, Notes on separability of -algebras, Taiwanese Journal of mathematics, Vol 16, No 2 (2012) (web)
George A. Elliott, Ilijas Farah, Vern Paulsen, Christian Rosendal, Andrew S. Toms, Asger Törnquist, The isomorphism relation for separable C-algebras_ (arXiv:1301.7108)
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