Stability of the gapless pure point spectrum of self-adjoint operators

Abstract

We consider a self-adjoint operator $T$ on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of $T$ and on the bounded perturbation $V$ ensuring the global stability of the spectral nature of $T+V$.

34 pages

References in corpus (1)

• Localization for Almost-Periodic Operators with Power-law Long-range Hopping: A Nash-Moser Iteration Type Reducibility Approach

Cited by in corpus (2)

• Robustness of quantum symmetries against perturbations
• Perturbative diagonalization and spectral gaps of quasiperiodic operators on ${\ell }^2({\mathbb{Z}}^d)$ with monotone potentials