 Theorem.If the C*-algebra formula_11 acts topologically irreducibly on the Hilbert space formula_12 is a set of vectors and formula_13 is a linearly independent set of vectors in formula_2, there is an formula_15 in formula_11 such that formula_17.If formula_18 for some self-adjoint operator formula_19, then formula_15 can be chosen to be self-adjoint.