Commutator estimates in $W^*$-factors

Details Commutator estimates in $W^*$-factors Commutator estimates in $W^*$-factors

2010-08-19

arxiv.org/abs/1008.3210v1

Mathematics

Operator Algebras

21 pages

Scientific paper

Let $\mathcal{M}$ be a $W^*$-factor and let $S\left( \mathcal{M} \right) $ be the space of all measurable operators affiliated with $\mathcal{M}$. It is shown that for any self-adjoint element $a\in S(\mathcal{M})$ there exists a scalar $\lambda_0\in\mathbb{R}$, such that for all $\varepsilon > 0$, there exists a unitary element $u_\varepsilon$ from $\mathcal{M}$, satisfying $|[a,u_\varepsilon]| \geq (1-\varepsilon)|a-\lambda_0\mathbf{1}|$. A corollary of this result is that for any derivation $\delta$ on $\mathcal{M}$ with the range in an ideal $I\subseteq\mathcal{M}$, the derivation $\delta$ is inner, that is $\delta(\cdot)=\delta_a(\cdot)=[a,\cdot]$, and $a\in I$. Similar results are also obtained for inner derivations on $S(\mathcal{M})$.

Affiliated with

Also associated with

No associations

Rating

Commutator estimates in $W^*$-factors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Commutator estimates in $W^*$-factors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Commutator estimates in $W^*$-factors will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-134559