On a question of Brown, Douglas, and Fillmore

In this note we answer an old question of Brown, Douglas, and Fillmore [L. Brown, R.G. Douglas, P. Fillmore, Unitary equivalence modulo the compact operators and extensions of C∗-algebras, in: Proc. Conf. Operator Theory, in: Lecture Notes in Math., vol. 345, Springer, Berlin, 1973, pp. 58–128]. © 2007 Elsevier Inc. All rights reserved.