Weakly $\mathcal U(d)$-homogeneous commuting tuple of bounded operators
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917135252455424 |
|---|---|
| author | Ghara, Soumitra Kumar, Surjit Trivedi, Shailesh |
| author_facet | Ghara, Soumitra Kumar, Surjit Trivedi, Shailesh |
| contents | We introduce and study the weakly $\mathcal U(d)$-homogeneous commuting tuple of operators. We provide a sufficient condition under which a weakly $\mathcal U(d)$-homogeneous tuple is similar to a $\mathcal U(d)$-homogeneous tuple. Further, we focus our attention to multishifts and completely characterize weakly $\mathcal U(d)$-homogeneous multishifts. In particular, we show that a multishift is weakly $\mathcal U(d)$-homogeneous if and only if it similar to a $\mathcal U(d)$-homogeneous multishift. The results for multishifts are further refined for the class of spherically balanced multishifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weakly $\mathcal U(d)$-homogeneous commuting tuple of bounded operators Ghara, Soumitra Kumar, Surjit Trivedi, Shailesh Functional Analysis Primary 47A13, 47B37, Secondary 47B32 We introduce and study the weakly $\mathcal U(d)$-homogeneous commuting tuple of operators. We provide a sufficient condition under which a weakly $\mathcal U(d)$-homogeneous tuple is similar to a $\mathcal U(d)$-homogeneous tuple. Further, we focus our attention to multishifts and completely characterize weakly $\mathcal U(d)$-homogeneous multishifts. In particular, we show that a multishift is weakly $\mathcal U(d)$-homogeneous if and only if it similar to a $\mathcal U(d)$-homogeneous multishift. The results for multishifts are further refined for the class of spherically balanced multishifts. |
| title | Weakly $\mathcal U(d)$-homogeneous commuting tuple of bounded operators |
| topic | Functional Analysis Primary 47A13, 47B37, Secondary 47B32 |
| url | https://arxiv.org/abs/2512.08649 |