On a Weyl-von Neumann type theorem for antilinear self-adjoint operators

• Autorzy: Santtu Ruotsalainen
• Języki publikacji: EN

Abstrakty

EN

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. On the way, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators is constructed.

Kategorie tematyczne

• 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
• 47A55: Perturbation theory
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 213
• Numer: 3
• Strony: 191-205

Daty

wydano

2012

Twórcy

autor

Santtu Ruotsalainen

• Institute of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland

Identyfikatory

DOI

10.4064/sm213-3-1