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

Tom 213 / 2012

Santtu Ruotsalainen Studia Mathematica 213 (2012), 191-205 MSC: Primary 47A55; Secondary 47B10, 47B15. DOI: 10.4064/sm213-3-1

Streszczenie

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.

Autorzy

  • Santtu RuotsalainenInstitute of Mathematics
    Aalto University
    P.O. Box 11100
    FI-00076 Aalto, Finland
    e-mail

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