Mathematics – Operator Algebras
Scientific paper
2007-07-28
Mathematics
Operator Algebras
42 pages, the introduction is rewritten, minor corrections
Scientific paper
Let $\M$ be a semi-finite factor and let $\J(\M)$ be the set of operators $T$ in $\M$ such that $T=ETE$ for some finite projection $E$. In this paper we obtain a representation theorem for unitarily invariant norms on $\J(\M)$ in terms of Ky Fan norms. As an application, we prove that the class of unitarily invariant norms on $\J(\M)$ coincides with the class of symmetric gauge norms on a classical abelian algebra, which generalizes von Neumann's classical result \cite{vN} on unitarily invariant norms on $M_n(\cc)$. As another application, Ky Fan's dominance theorem \cite{Fan} is obtained for semi-finite factors. Some classical results in non-commutative $L^p$-theory (e.g., non-commutative H$\ddot{\text{o}}$lder's inequality, duality and reflexivity of non-commutative $L^p$-spaces) are extended to general unitarily invariant norms related to semi-finite factors. We also prove that up to a scale the operator norm is the unique unitarily invariant norm associated to a type ${\rm III}$ factor.
Fang Junsheng
Hadwin Don
No associations
LandOfFree
Unitarily invariant norms related to 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 Unitarily invariant norms related to factors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unitarily invariant norms related to factors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-396119