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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-3-1,
author = {Santtu Ruotsalainen},
title = {On a Weyl-von Neumann type theorem for antilinear self-adjoint operators},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {191-205},
zbl = {1304.47018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-3-1}
}
Santtu Ruotsalainen. On a Weyl-von Neumann type theorem for antilinear self-adjoint operators. Studia Mathematica, Tome 209 (2012) pp. 191-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-3-1/