On a weyl-von neumann type theorem for antilinear self-adjoint operators
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On a weyl-von neumann type theorem for antilinear self-adjoint operators. / Ruotsalainen, Santtu.
In: Studia Mathematica, Vol. 213, No. 3, 2012, p. 191-205.Research output: Contribution to journal › Article › Scientific › peer-review
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TY - JOUR
T1 - On a weyl-von neumann type theorem for antilinear self-adjoint operators
AU - Ruotsalainen, Santtu
PY - 2012
Y1 - 2012
N2 - 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.
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.
KW - Antilinear operator
KW - Conjugation
KW - Diagonalizable operator
KW - Weyl-von neumann theorem
UR - http://www.scopus.com/inward/record.url?scp=84874076167&partnerID=8YFLogxK
U2 - 10.4064/sm213-3-1
DO - 10.4064/sm213-3-1
M3 - Article
VL - 213
SP - 191
EP - 205
JO - Studia Mathematica
JF - Studia Mathematica
SN - 0039-3223
IS - 3
ER -
ID: 12921078
