# On a weyl-von neumann type theorem for antilinear self-adjoint operators

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**On a weyl-von neumann type theorem for antilinear self-adjoint operators.** / Ruotsalainen, Santtu.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Studia Mathematica*, vol. 213, no. 3, pp. 191-205. https://doi.org/10.4064/sm213-3-1

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*Studia Mathematica*,

*213*(3), 191-205. https://doi.org/10.4064/sm213-3-1

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TY - JOUR

T1 - On a weyl-von neumann type theorem for antilinear self-adjoint operators

AU - Ruotsalainen, Santtu

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Antilinear operator

KW - Conjugation

KW - Diagonalizable operator

KW - Weyl-von neumann theorem

UR - http://www.scopus.com/inward/record.url?scp=84874076167&partnerID=8YFLogxK

U2 - 10.4064/sm213-3-1

DO - 10.4064/sm213-3-1

M3 - Article

VL - 213

SP - 191

EP - 205

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

IS - 3

ER -

ID: 12921078