  Helium in nanoporous media has attracted much interest as a model Bose system
with disorder and confinement. Here we have examined how a change in porous
structure by preplating a monolayer of krypton affects the superfluid
properties of $^4$He adsorbed or confined in a nanoporous Gelsil glass, which
has a three-dimensional interconnected network of nanopores of 5.8 nm in
diameter. Isotherms of adsorption and desorption of nitrogen show that
monolayer preplating of Kr decreases the effective pore diameter to 4.7 nm and
broadens the pore size distribution by about eight times from the sharp
distribution of the bare Gelsil sample. The superfluid properties were studied
by a torsional oscillator for adsorbed film states and pressurized liquid
states, both before and after the monolayer Kr preplating. In the film states,
both the superfluid transition temperature $T_{\mathrm c}$ and the superfluid
density decrease about 10 percent by Kr preplating. The suppression of film
superfluidity is attributed to the quantum localization of $^4$He atoms by the
randomness in the substrate potential, which is caused by the
preplating--induced broadening of the pore size distribution. In the
pressurized liquid states, the superfluid density $\rho_{\mathrm s}$ is found
to increase by 10 percent by Kr preplating, whereas $T_{\mathrm c}$ is
decreased by 2 percent at all pressures. The unexpected enhancement of
$\rho_{\mathrm s}$ might indicate the existence of an unknown disorder effect
for confined $^4$He.
