Domination of semigroups on standard forms of von Neumann algebras
| Autor: | Arora, Sahiba, Chill, Ralph, Srivastava, Sachi |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Archiv der Mathematik, vol. 121, pp. 715-729 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00013-023-01946-y |
| Popis: | 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. Comment: This is version 2. Compared to version 1, a reference has been added along with several minor changes |
| Databáze: | arXiv |
| Externí odkaz: |
|