Finite rank perturbations and solutions to the operator Riccati equation
Abstract
We consider an off-diagonal self-adjoint finite rank perturbation of a self-adjoint operator in a complex separable Hilbert space $\mathfrak{H}_0 \oplus \mathfrak{H}_1$, where $\mathfrak{H}_1$ is finite dimensional. We describe the singular spectrum of the perturbed operator and establish a connection with solutions to the operator Riccati equation. In particular, we prove existence results for solutions in the case where the whole Hilbert space is finite dimensional.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2014
- DOI:
- 10.48550/arXiv.1403.5527
- arXiv:
- arXiv:1403.5527
- Bibcode:
- 2014arXiv1403.5527G
- Keywords:
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- Mathematics - Spectral Theory;
- Mathematics - Functional Analysis;
- 47A62;
- 47A55;
- 47B15
- E-Print:
- 13 pages, added Preliminaries, added more details