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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.
Santtu Ruotsalainen. "On a Weyl-von Neumann type theorem for antilinear self-adjoint operators." Studia Mathematica 213.3 (2012): 191-205. <http://eudml.org/doc/285451>.
@article{SanttuRuotsalainen2012, 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.}, author = {Santtu Ruotsalainen}, journal = {Studia Mathematica}, keywords = {antilinear operator; diagonalizable operator; Weyl-von Neumann theorem; conjugation}, language = {eng}, number = {3}, pages = {191-205}, title = {On a Weyl-von Neumann type theorem for antilinear self-adjoint operators}, url = {http://eudml.org/doc/285451}, volume = {213}, year = {2012}, }
TY - JOUR AU - Santtu Ruotsalainen TI - On a Weyl-von Neumann type theorem for antilinear self-adjoint operators JO - Studia Mathematica PY - 2012 VL - 213 IS - 3 SP - 191 EP - 205 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. LA - eng KW - antilinear operator; diagonalizable operator; Weyl-von Neumann theorem; conjugation UR - http://eudml.org/doc/285451 ER -