On Specht's Theorem in UHF C?-algebras

Specht's Theorem states that two matrices A and B in M n ( C ) are unitarily equivalent if only tr w , ? = for all words x y non-commuting variables . In this article we examine to what extent trace condition characterises approximate unitary equivalence uniformly hyperfinite (UHF) -algebras. particular, show given elements a b of the universal UHF-algebra Q which generate -algebras satisfying UCT, they approximately ? (where denotes unique tracial state on ), while there exist 2 ? fail be despite fact satisfy condition. We also consequence these results ampliations matrices.