In mathematics, the spectrum of a C*-algebra or dual of a C*-algebra A, denoted Â, is the set of unitary equivalence classes of irreducible *-representations of A. A *-representation π of A on a Hilbert space H is irreducible if, and only if, there is no closed subspace K different from H and {0} which is invariant under all operators π with x ∈ A. We implicitly assume that irreducible representation means non-null irreducible representation, thus excluding trivial representations on one-dimensional spaces. Wikipedia