  Antilinear operators on a complex Hilbert space arise in various contexts in
mathematical physics. In this paper, an analogue of the Weyl--von Neumann
theorem for antilinear self-adjoint operators is proved, i.e. that an
antilinear self-adjoint operator is the sum of a diagonalizable operator and of
a compact operator with arbitrarily small Schatten $p$-norm. In doing so, we
discuss conjugations and their properties. A spectral integral representation
for antilinear self-adjoint operators is constructed.
