Comparison of topologies on *-algebras of locally measurable operators
Abstract
We consider the locally measure topology $t(\mathcal{M})$ on the *-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated with a von Neumann algebra $\mathcal{M}$. We prove that $t(\mathcal{M})$ coincides with the $(o)$-topology on $LS_h(\mathcal{M})=\{T\in LS(\mathcal{M}): T^*=T\}$ if and only if the algebra $\mathcal{M}$ is $\sigma$-finite and a finite algebra. We study relationships between the topology $t(\mathcal{M})$ and various topologies generated by faithful normal semifinite traces on $\mathcal{M}$.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2010
- DOI:
- 10.48550/arXiv.1001.1651
- arXiv:
- arXiv:1001.1651
- Bibcode:
- 2010arXiv1001.1651C
- Keywords:
-
- Mathematics - Operator Algebras;
- 46L50;
- 47D25;
- 47D40;
- 06F25;
- 06F30
- E-Print:
- 21 pages