Random perturbations of singular spectra

Random perturbations of singular spectra
HTML articles powered by AMS MathViewer

by James S. Howland PDF

Proc. Amer. Math. Soc. 112 (1991), 1009-1011 Request permission

The singular parts of the self-adjoint operators $T$ and $H = T + V$ are mutually singular for "almost every" bounded perturbation $V$.

References

William F. Donoghue Jr., On the perturbation of spectra, Comm. Pure Appl. Math. 18 (1965), 559–579. MR 190761, DOI 10.1002/cpa.3160180402
James S. Howland, Perturbation theory of dense point spectra, J. Funct. Anal. 74 (1987), no. 1, 52–80. MR 901230, DOI 10.1016/0022-1236(87)90038-3
Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959
Barry Simon and Tom Wolff, Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Comm. Pure Appl. Math. 39 (1986), no. 1, 75–90. MR 820340, DOI 10.1002/cpa.3160390105