Trace-class perturbation and strong convergence: Wave operators revisited

Xia, Jingbo

doi:10.1090/S0002-9939-00-05907-4

Trace-class perturbation and strong convergence: Wave operators revisited
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Proc. Amer. Math. Soc. 128 (2000), 3519-3522 Request permission

Abstract:

We give a new construction of wave operators for a self-adjoint operator under trace-class perturbation. This construction requires no quantitative estimates.

References

Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
Tosio Kato, Perturbation theory for linear operators, 2nd ed., Grundlehren der Mathematischen Wissenschaften, Band 132, Springer-Verlag, Berlin-New York, 1976. MR 0407617
Michael Reed and Barry Simon, Methods of modern mathematical physics. III, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. Scattering theory. MR 529429
Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
Dan Voiculescu, Some results on norm-ideal perturbations of Hilbert space operators. II, J. Operator Theory 5 (1981), no. 1, 77–100. MR 613049
Dan Voiculescu, Hilbert space operators modulo normed ideals, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 1041–1047. MR 804756
Jürgen Voigt, Perturbation theory for commutative $m$-tuples of self-adjoint operators, J. Functional Analysis 25 (1977), no. 4, 317–334. MR 0451011, DOI 10.1016/0022-1236(77)90040-4