Shear viscosity of degenerate electron matter

We calculate the partial electron shear viscosity ${\eta }_{ee}$ limited by electron-electron collisions in a strongly degenerate electron gas taking into account the Landau damping of transverse plasmons. The Landau damping strongly suppresses ${\eta }_{ee}$ in the domain of ultrarelativistic degenerate electrons and modifies its %asymptotic temperature behavior. The efficiency of the electron shear viscosity in the cores of white dwarfs and envelopes of neutron stars is analyzed.