Tridiagonal matrix representations of cyclic self-adjoint operators. II
J. Dombrowski · Pacific Journal of Mathematics · 1985
A bounded cyclic self-adjoint operator C defined on a separable Hilbert space H can be represented as a tridiagonal matrix with respect to the basis generated by the cyclic vector.An operator / can then be defined so that CJ -JC = -2iK where K also has tridiagonal form.If the subdiagonal elements of C converge to a non-zero limit and if K is of trace class then C must have an absolutely continuous part.