The Weyl-von Neumann theorem in von Neumann factors

• Autorzy: Kamiński K.

Identyfikatory

DOI

10.1515/jaa-2017-0006

• Języki publikacji: EN

Abstrakty

EN

In a von Neumann factor M of type II_∞ with semifinite faithful normal trace τ, the q-th Schattentype norm ‖·‖_q of an operator A ϵ M is defined as ‖A‖_q = (τ(|A|^q))^1/q.We will prove that for every self-adjoint operator H ϵ M and any numbers q > 1, ε > 0, there exists a self-adjoint perturbation operator A ϵ M such that ‖A‖ < ε, ‖A‖_q < ε and H + A has a pure point spectrum.We will also discuss the possibility of transferring this result onto other von Neumann factors.

Słowa kluczowe

EN

von Neumann factor; perturbation of linear operator; pure point spectrum; Schatten-type norm

PL

faktor von Neumanna; perturbacje operatorów liniowych; norma Schattena

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2017
• Tom: Vol. 23, nr 1
• Strony: 39--42
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Kamiński K.

• Faculty of Navigation, Gdynia Maritime University, Morska 81-87, 81-225 Gdynia, Poland

Bibliografia

• [1] V. Kaftal,On the theory of compact operators in von Neumann algebras. II, Pacific J. Math. 79 (1978), no. 1, 129-137.
• [2] T. Kato, Perturbation of continuous spectra by trace class operators, Proc. Japan Acad. 33 (1957), 260-264.
• [3] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1995.
• [4] S. T. Kuroda, On a theorem of Weyl-von Neumann, Proc. Japan Acad. 34 (1958), no. 1, 11-15.
• [5] R. Schatten, Norm Ideals of Completely Continuous Operators, Springer, Berlin, 1960.
• [6] B. Simon, Trace Ideals and their Applications, Cambridge University Press, Cambridge, 1979.
• [7] S. Stratila and L. Zsido, Lectures on von Neumann Algebras, Editura Academiei, Bucharest, 1979.
• [8] M. Takesaki, Theory of Operator Algebras I, Springer, Berlin, 2002.
• [9] L. Zsidó, The Weyl-von Neumann theorem in semifinite factors, J. Funct. Anal. 18 (1975), no. 1, 60-72.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).