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

Santtu Ruotsalainen*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)191-205
Number of pages15
JournalStudia Mathematica
Volume213
Issue number3
DOIs
Publication statusPublished - 2012
MoE publication typeA1 Journal article-refereed

Keywords

  • Antilinear operator
  • Conjugation
  • Diagonalizable operator
  • Weyl-von neumann theorem

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