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

Santtu Ruotsalainen¹

¹ Institute of Mathematics Aalto University P.O. Box 11100 FI-00076 Aalto, Finland

Studia Mathematica, Tome 213 (2012) no. 3, pp. 191-205

Résumé

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.

Détail

DOI : 10.4064/sm213-3-1

Keywords: antilinear operators complex hilbert space arise various contexts mathematical physics paper analogue weyl von neumann theorem antilinear self adjoint operators proved antilinear self adjoint operator sum diagonalizable operator compact operator arbitrarily small schatten p norm discuss conjugations their properties spectral integral representation antilinear self adjoint operators constructed