Article
| Title: | The Wold-type decomposition and the kernel condition for quasi-isometries (English) |
| Author: | Stoica, Andra-Maria |
| Author: | Suciu, Laurian |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 3 |
| Year: | 2025 |
| Pages: | 1049-1072 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | This paper investigates the necessary and sufficient conditions under which a quasi-isometry $T$ on a Hilbert space ${\mathcal H}$ admits a Wold-type decomposition in Shimorin's sense. We establish a close connection between this decomposition and the kernel condition $T^*T {\mathcal N} (T^*)\subset {\mathcal N} (T^*)$, where ${\mathcal N}(T^*)$ is the kernel of the adjoint operator $T^*$ of $T$. Additionally, we discuss conditions related to certain cyclic and wandering subspaces, as well as the role of the Cauchy dual operator of $T$. Furthermore, we examine operators similar to contractions, that admit quasi-isometric liftings satisfying the kernel condition. This analysis leads to the identification of a special class of quasicontractions with such liftings, and on the other hand, to the construction of certain expansive quasi-isometric liftings $S_{\alpha }$ ($0<\alpha <1)$. (English) |
| Keyword: | Wold-type decomposition |
| Keyword: | quasi-isometry |
| Keyword: | lifting |
| MSC: | 47A05 |
| MSC: | 47A15 |
| MSC: | 47A20 |
| MSC: | 47A63 |
| DOI: | 10.21136/CMJ.2025.0071-25 |
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| Date available: | 2025-09-19T12:09:45Z |
| Last updated: | 2025-09-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153066 |
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