  The tensor and exterior squares of a completely continuous non-negative
linear operator $A$ acting in the ideal space $X(\Omega)$ are studied. The
theorem representing the point spectrum (except, probably, zero) of the tensor
square $A \otimes A$ in the terms of the spectrum of the initial operator $A$
is proved. The existence of the second (according to the module) positive
eigenvalue $\lambda_2$, or a pair of complex adjoint eigenvalues of a
completely continuous non-negative operator $A$ is proved under the additional
condition, that its exterior square $A\wedge A$ is also nonnegative.
