  In this paper, we present a characterization of optimal entanglement
witnesses in terms of positive maps and then provide a general method of
checking optimality of entanglement witnesses. Applying it, we obtain new
indecomposable optimal witnesses which have no spanning property. These also
provide new examples which support a recent conjecture saying that the
so-called structural physical approximations to optimal positive maps (optimal
entanglement witnesses) give entanglement breaking maps (separable states).
