  Detections of planets in eccentric, close (separations of ~20 AU) binary
systems such as \alpha Cen or \gamma Cep provide an important test of planet
formation theories. Gravitational perturbations from the companion are expected
to excite high planetesimal eccentricities resulting in destruction, rather
than growth, of objects with sizes of up to several hundred km in collisions of
similar-size bodies. It was recently suggested that gravity of a massive
axisymmetric gaseous disk in which planetesimals are embedded drives rapid
precession of their orbits, suppressing eccentricity excitation. However, disks
in binaries are themselves expected to be eccentric, leading to additional
planetesimal excitation. Here we develop secular theory of eccentricity
evolution for planetesimals perturbed by the gravity of an elliptical
protoplanetary disk (neglecting gas drag) and the companion. For the first time
we derive an expression for the disturbing function due to an eccentric disk,
which can be used for a variety of other astrophysical problems. We obtain
explicit analytical solutions for planetesimal eccentricity evolution and
delineate four different regimes of dynamical excitation. We show that in
systems with massive (>10^{-2}M_Sun) disks, planetesimal eccentricity is
usually determined by the gravity of the eccentric disk alone, and is
comparable to the disk eccentricity. As a result, the latter imposes a lower
limit on collisional velocities of solids, making their growth problematic.
This fragmentation barrier can be removed if the gaseous disk rapidly precesses
or if its own self-gravity is efficient at lowering disk eccentricity.
