  Real linear operators emerge in a range of mathematical physics applications.
In this paper spectral questions of compact real linear operators are
addressed. A Lomonosov-type invariant subspace theorem for antilinear compact
operators is proved. Properties of the characteristic polynomial of a finite
rank real linear operator are investigated. A related numerical function,
defined as a normalization of the characteristic polynomial, is studied. An
extension to trace-class operators is discussed.
