Compact real linear operators

TL;DR

This paper investigates spectral properties of compact real linear operators, proving an invariant subspace theorem for antilinear operators, analyzing characteristic polynomials, and extending results to trace-class operators.

Contribution

It introduces a Lomonosov-type invariant subspace theorem for antilinear compact operators and studies characteristic polynomials of finite rank real linear operators.

Findings

Proved an invariant subspace theorem for antilinear compact operators

Analyzed properties of the characteristic polynomial of finite rank real linear operators

Extended spectral analysis to trace-class 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.