arXiv subjects

Santtu Ruotsalainen

Publications and source records attributed to Santtu Ruotsalainen.

2 recordsLinked to original sources

arXiv2013

Compact real linear operators

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.

math.SP↗

arXiv2012

On a Weyl-von Neumann -type Theorem for Antilinear Self-adjoint Operators

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.

math.SP↗