The Failure of Approximate Inner Conjugacy for Standard Diagonals in Regular Limit Algebras

Abstract

AbstractAF C*-algebras contain natural AF masas which, here, we call standard diagonals. Standard diagonals are unique, in the sense that two standard diagonals in an AF C*-algebra are conjugate by an approximately inner automorphism. We show that this uniqueness fails for non-selfadjoint AF operator algebras. Precisely, we construct two standard diagonals in a particular non-selfadjoint AF operator algebra which are not conjugate by an approximately inner automorphism of the non-selfadjoint algebra.