Conjugating by singular operators: On the boundedness of similarity transforms near singular points
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914988343427072 |
|---|---|
| author | Falkowski, Daniel Lidgren, Carl-Fredrik |
| author_facet | Falkowski, Daniel Lidgren, Carl-Fredrik |
| contents | We consider the question of, given operators $A$, $Z$ and a sequence of invertible operators $U_n\to Z$, whether the sequence $U_nAU_n^{-1}$ is bounded in norm, as well as generalizations of this where $U_nAU_n^{-1}$ is modified by some bounded linear map on bounded linear operators. In the setting of Hilbert spaces, we provide a complete classification in terms of algebraic criteria of those $A$ for which such a sequence exists, as long as $Z$ is of generalized index zero, which always holds in finite-dimensional contexts. In the process, we prove that particular coefficients arising in inverses of certain good paths going to $Z$ can also be classified in terms of an entirely algebraic criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conjugating by singular operators: On the boundedness of similarity transforms near singular points Falkowski, Daniel Lidgren, Carl-Fredrik Functional Analysis 46C05, 46C07, 47L05, 47L30, 47A15 We consider the question of, given operators $A$, $Z$ and a sequence of invertible operators $U_n\to Z$, whether the sequence $U_nAU_n^{-1}$ is bounded in norm, as well as generalizations of this where $U_nAU_n^{-1}$ is modified by some bounded linear map on bounded linear operators. In the setting of Hilbert spaces, we provide a complete classification in terms of algebraic criteria of those $A$ for which such a sequence exists, as long as $Z$ is of generalized index zero, which always holds in finite-dimensional contexts. In the process, we prove that particular coefficients arising in inverses of certain good paths going to $Z$ can also be classified in terms of an entirely algebraic criterion. |
| title | Conjugating by singular operators: On the boundedness of similarity transforms near singular points |
| topic | Functional Analysis 46C05, 46C07, 47L05, 47L30, 47A15 |
| url | https://arxiv.org/abs/2410.19161 |