Let X be a pointed space. If I define Σ^∞X be the Ω-spectrum whose n-th space is QΣ^nX, is there a simple direct proof that Map(Σ^∞X,E)=Map(X,Ω^∞E) for any Ω-spectrum E? Here the mapping space in spectra is defined as the (homotopy) limit along the obvious tower
