Morita Equivalence

Modifying a C*-algebra A by replacing it with \(M_2(A)\) or \(M_n (A)\) or \(A\otimes \mathcal {K}\) has little impact on the structure theory of the C*-algebra. It therefore seems reasonable to consider a pair of C*-algebras A and B to be equivalent if \(A\otimes \mathcal {K}\) and \(B\otimes \mathcal {K}\) are isomorphic.