K-Theory and Perturbations of Absolutely Continuous Spectra

Trace Class Perturbations and the Absence of Absolutely Continuous Spectra

We show that various Hamiltonians and Jacobi matrices have no absolutely continuous spectrum by showing that under a trace class perturbation they become a direct sum of finite matrices.

Wiener - Hopf Operators and Absolutely Continuous Spectra

CONTINUOUS SPECTRA. II BY C. R. PUTNAM Communicated by Maurice Heins, November 1, 1967 1. This paper is a continuation of [4]. It may be recalled that if A is a self-adjoint operator on a Hubert space § with spectral resolution A=zf\dE\, then the set of elements x in § for which ||-Ex#|| is an absolutely continuous function of X is a subspace, &a(A), of § (see, e.g., Halmos [l, p. 104]). The op...

Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder

We consider the Laplacian on a rooted metric tree graph with branching number K ≥ 2 and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generali...

Topological K-theory of Algebraic K-theory Spectra

One of the central problems of algebraic K-theory is to compute the K-groups KX of a scheme X. Since these groups are, by definition, the homotopy groups of a spectrum KX, it makes sense to analyze the homotopy-type of the spectrum, rather than just the disembodied homotopy groups. In addition to facilitating the computation of the K-groups themselves, knowledge of the spectrum KX can be applie...

On Absolutely Continuous Transformations