Irreducible representations of the 𝐶*-algebra generated by a quasinormal operator

Abstract

For A a quasinormal operator on Hilbert space, we determine the irreducible representations of C ∗ ( A ) {C^ \ast }(A) , the C ∗ {C^ \ast } -algebra generated by A and the identity. We also explicitly describe the topology on the space of unitary equivalence classes of irreducible representations of C ∗ ( A ) {C^ \ast }(A) and calculate the regularized transform of C ∗ ( A ) {C^ \ast }(A) , thus exhibiting an isomorphic copy of C ∗ ( A ) {C^ \ast }(A) .