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We study the spectral density function of a two-dimensional electron liquidin a weak magnetic field, the filling factor $\nu\gg 1$. A hydrodynamic modelfor low-energy excitations of the liquid is developed. It is found that even at$\nu\gg 1$ the density of states exhibits a gap at low energies. Its width$2E_0$ depends on the strength of interaction only logarithmically,$2E_0=(\hbar\omega_c/\nu)\ln (\nu e^2/\varepsilon\hbar v_F)$. The effects oftemperature and disorder on the density of states are discussed.Comment: 8 pages, preprint TPI-MINN-94/28-

Tunneling into a Two-Dimensional Electron Liquid in a Weak Magnetic Field