On a Weyl–von Neumann type theorem for antilinear self-adjoint operators
Volume 213 / 2012
Studia Mathematica 213 (2012), 191-205
MSC: Primary 47A55; Secondary 47B10, 47B15.
DOI: 10.4064/sm213-3-1
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.
