Given a separable strongly self-concordant function f:Rn -> R, we show the associated spectral function F(X)= (foL)(X) is also strongly self-concordant function. In addition, there is a universal constant O such that, if f(x) is separable self-concordant barrier then O^2F(X) is a self-concordant barrier. We estimate that for the universal constant we have O<=22. This generalizes the relationship between the standard logarithmic barriers -log(x1)-...-log(xn) and -log det(X) and gives a partial solution to a conjecture of L. Tuncel.
Submitted for publication in Mathematical Programming