Compact real linear operators

Abstract

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.