On a Weyl-von Neumann -type Theorem for Antilinear Self-adjoint Operators

2012/03/21 by Ruotsalainen, Santtu
#FOS: Mathematics #Primary 47A10 #Secondary 47B38 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1203.4670

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. In doing so, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators is constructed.

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