Root System of a Perturbation of a Selfadjoint Operator with Discrete Spectrum

Details Root System of a Perturbation of a Selfadjoint Operator with Discrete Spectrum Root System of a Perturbation of a Selfadjoint Operator with Discrete Spectrum

2011-04-05

arxiv.org/abs/1104.0915v1

Mathematics

Spectral Theory

Scientific paper

We analyze the perturbations $T+B$ of a selfadjoint operator $T$ in a Hilbert space $H$ with discrete spectrum $\{t_k \}$, $T \phi_k = t_k \phi_k$, as an extension of our constructions in arXiv: 0912.2722 where $T$ was a harmonic oscillator operator. In particular, if $t_{k+1}-t_k \geq c k^{\alpha - 1}, \quad \alpha > 1/2$ and $\| B \phi_k \| = o(k^{\alpha - 1})$ then the system of root vectors of $T+B$, eventually eigenvectors of geometric multiplicity 1, is an unconditional basis in $H$.

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