The singularly continuous spectrum and non-closed invariant subspaces
| dc.creator | Kostrykin, Vadim | |
| dc.creator | Makarov, Konstantin A. | |
| dc.date | 2004-03-05 | |
| dc.date | 2004-07-28 | |
| dc.date.accessioned | 2026-07-07T06:21:50Z | |
| dc.date.available | 2026-07-07T06:21:50Z | |
| dc.description | Let $\mathbf{A}$ be a bounded self-adjoint operator on a separable Hilbert space $\mathfrak{H}$ and $\mathfrak{H}_0\subset\mathfrak{H}$ a closed invariant subspace of $\mathbf{A}$. Assuming that $\mathfrak{H}_0$ is of codimension 1, we study the variation of the invariant subspace $\mathfrak{H}_0$ under bounded self-adjoint perturbations $\mathbf{V}$ of $\mathbf{A}$ that are off-diagonal with respect to the decomposition $\mathfrak{H}= \mathfrak{H}_0\oplus\mathfrak{H}_1$. In particular, we prove the existence of a one-parameter family of dense non-closed invariant subspaces of the operator $\mathbf{A}+\mathbf{V}$ provided that this operator has a nonempty singularly continuous spectrum. We show that such subspaces are related to non-closable densely defined solutions of the operator Riccati equation associated with generalized eigenfunctions corresponding to the singularly continuous spectrum of $\mathbf{B}$. | |
| dc.identifier | https://arxiv.org/abs/math/0403112 | |
| dc.identifier | http://arxiv.org/abs/math/0403112 | |
| dc.identifier | Operator Theory: Advances and Applications, Vol. 160, Birkhauser, Basel, 2005, p. 299 - 309. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95730 | |
| dc.subject | Spectral Theory | |
| dc.subject | 47A55; 47A15; 47B15 | |
| dc.title | The singularly continuous spectrum and non-closed invariant subspaces | |
| dc.type | text |