On Mixing and Completely Mixing Properties of Positive $L^1$-Contractions of Finite Von Neumann Algebras
| dc.creator | Mukhamedov, Farrukh | |
| dc.creator | Temir, Seyit | |
| dc.creator | Akin, Hasan | |
| dc.date | 2005-10-16 | |
| dc.date.accessioned | 2026-07-07T06:47:32Z | |
| dc.date.available | 2026-07-07T06:47:32Z | |
| dc.description | Akcoglu and Suchaston proved the following result: Let $T:L^1(X,{\cf},\m)\to L^1(X,{\cf},\m)$ be a positive contraction. Assume that for $z\in L^1(X,{\cf},\m)$ the sequence $(T^nz)$ converges weakly in $L^1(X,{\cf},\m)$, then either $\lim\limits_{n\to\infty}\|T^nz\|=0$ or there exists a positive function $h\in L^1(X,{\cf},\m)$, $h\neq 0$ such that $Th=h$. In the paper we prove an extension of this result in finite von Neumann algebra setting, and as a consequence we obtain that if a positive contraction of a noncommutative $L^1$-space has no non zero positive invariant element, then its mixing property implies completely mixing property one. | |
| dc.description | 9 pages. Accepted for publication in Proc. AMS | |
| dc.identifier | https://arxiv.org/abs/math/0510336 | |
| dc.identifier | http://arxiv.org/abs/math/0510336 | |
| dc.identifier | Proc. Amer. Math. Soc. 134 (2006), N.3, 843--850. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103686 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 47A35, 28D05 | |
| dc.title | On Mixing and Completely Mixing Properties of Positive $L^1$-Contractions of Finite Von Neumann Algebras | |
| dc.type | text |