Domination of semigroups on standard forms of von Neumann algebras
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911835208286208 |
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| author | Arora, Sahiba Chill, Ralph Srivastava, Sachi |
| author_facet | Arora, Sahiba Chill, Ralph Srivastava, Sachi |
| contents | Consider $(T_t)_{t\ge 0}$ and $(S_t)_{t\ge 0}$ as real $C_0$-semigroups generated by closed and symmetric sesquilinear forms on a standard form of a von Neumann algebra. We provide a characterisation for the domination of the semigroup $(T_t)_{t\ge 0}$ by $(S_t)_{t\ge 0}$, which means that $-S_t v\le T_t u\le S_t v$ holds for all $t\ge 0$ and all real $u$ and $v$ that satisfy $-v\le u\le v$. This characterisation extends the Ouhabaz characterisation for semigroup domination to the non-commutative $L^2$ spaces. Additionally, we present a simpler characterisation when both semigroups are positive as well as consider the setting in which $(T_t)_{t\ge 0}$ need not be real. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02284 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Domination of semigroups on standard forms of von Neumann algebras Arora, Sahiba Chill, Ralph Srivastava, Sachi Operator Algebras Functional Analysis 47D06, 46L89, 47A07, 47B65, 47A15 Consider $(T_t)_{t\ge 0}$ and $(S_t)_{t\ge 0}$ as real $C_0$-semigroups generated by closed and symmetric sesquilinear forms on a standard form of a von Neumann algebra. We provide a characterisation for the domination of the semigroup $(T_t)_{t\ge 0}$ by $(S_t)_{t\ge 0}$, which means that $-S_t v\le T_t u\le S_t v$ holds for all $t\ge 0$ and all real $u$ and $v$ that satisfy $-v\le u\le v$. This characterisation extends the Ouhabaz characterisation for semigroup domination to the non-commutative $L^2$ spaces. Additionally, we present a simpler characterisation when both semigroups are positive as well as consider the setting in which $(T_t)_{t\ge 0}$ need not be real. |
| title | Domination of semigroups on standard forms of von Neumann algebras |
| topic | Operator Algebras Functional Analysis 47D06, 46L89, 47A07, 47B65, 47A15 |
| url | https://arxiv.org/abs/2309.02284 |