  We study the transverse susceptibility of the fully frustrated
antiferromagnetic Ising $\Delta$-chain, extending Minami's transfer-matrix
method for the transverse susceptibility of general-type Ising linear-chains
[JPSJ 67,1998,2255]. For transverse fields $\Gamma_1$ on tip spin sites and
$\Gamma_2$ on bottom spin sites, we calculate zero-field
transverse-susceptibilities $\chi_{tip}^x=\lim_{\Gamma_1,\Gamma_2 ->
0}M_{tip}^x/\Gamma_1$ and $\chi_{bottom}^x=\lim_{\Gamma_1,\Gamma_2 ->
0}M^x_{bottom}/\Gamma_2$, where $M_{tip (bottom)}^x$ denotes the magnetization
for tip (bottom) spin sites. Both the transverse susceptibilities follow
Curie's law at low temperatures. We also calculate
$\chi_{bottom}^x(\Gamma_1>0)$, transverse susceptibility of the bottom spin
chain under finite tip-spin transverse-fields, to understand the Curie type
behavior in the zero-field susceptibility. Using the second-order perturbation
theory, we discuss the $\Gamma_1$ dependence of $\chi_{bottom}^x(\Gamma_1)$ at
zero temperature.
