On the Kato-Rosenblum theorem

James Secord Howland

Vol. 123 (1986), No. 2, 329–335

DOI: 10.2140/pjm.1986.123.329

Abstract

The Kato-Rosenblum Theorem has no straightforward generalization to operators with non-absolutely continuous spectra. For example, if A is a bounded selfadjoint operator such that the singular continuous parts of H and H + A are unitarily equivalent for every selfadjoint operator H, then A = 0.

Mathematical Subject Classification 2000

Primary: 47A55

Secondary: 47B10

Milestones

Received: 8 March 1985

Published: 1 June 1986