Irreducible representations of the 𝐶*-algebra generated by an 𝑛-normal operator

Abstract

For A A an n n -normal operator on Hilbert space, we determine the irreducible representations of C ∗ ( A ) {C^ \ast }(A) , the C ∗ {C^ \ast } -algebra generated by A A and the identity. For A A a binormal operator, we determine an explicit description of the topology on the space of unitary equivalence classes of irreducible representations of C ∗ ( A ) {C^ \ast }(A) .