Weakly closed semigroups generated by operator-valued functions
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929306038435840 |
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| author | Ryzhikov, Valery V. |
| author_facet | Ryzhikov, Valery V. |
| contents | The function $P(T)=\sum_{i=0}^\infty c_i T^i$ is admissible if $c_i\geq 0$, $\sum_{i=0}^\infty c_i\leq 1$. For any given set of admissible functions $P_1,\dots, P_k$ there is a unitary operator $T$ of dynamic origin such that the weak closure of its powers is a semigroup generated by the operators $0$, $T$, $P_1(T),\dots, P_k(T)$, $T^\ast$, $P_1(T^\ast ),\dots, P_k(T^\ast)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weakly closed semigroups generated by operator-valued functions Ryzhikov, Valery V. Dynamical Systems The function $P(T)=\sum_{i=0}^\infty c_i T^i$ is admissible if $c_i\geq 0$, $\sum_{i=0}^\infty c_i\leq 1$. For any given set of admissible functions $P_1,\dots, P_k$ there is a unitary operator $T$ of dynamic origin such that the weak closure of its powers is a semigroup generated by the operators $0$, $T$, $P_1(T),\dots, P_k(T)$, $T^\ast$, $P_1(T^\ast ),\dots, P_k(T^\ast)$. |
| title | Weakly closed semigroups generated by operator-valued functions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2404.05706 |