T-duality of ZZ-brane

We examine how nonperturbative effects in string theory are transformed under the T-duality in its nonperturbative framework by analyzing the c=1/2 noncritical string theory as a simplest example. We show that in the T-dual theory they also take the form of exp(-S_0/g_s) in the leading order and that the instanton actions S_0 of the dual ZZ-branes are exactly the same as those in the original c=1/2 string theory. Furthermore we present formulas for coefficients of exp(-S_0/g_s) in the dual theory.