Mathematics – Operator Algebras
Scientific paper
2011-11-16
Mathematics
Operator Algebras
10 pages, no figures
Scientific paper
The carpenter problem in the context of $II_1$ factors, formulated by Kadison asks: Let $\mathcal{A} \subset \mathcal{M}$ be a masa in a type $II_1$ factor and let $E$ be the normal conditional expectation from $\mathcal{M}$ onto $\mathcal{A}$. Then, is it true that for every positive contraction $A$ in $\mathcal{A}$, there is a projection $P$ in $\mathcal{M}$ such that $E(P) = A$? In this note, we show that this is true if $A$ has finite spectrum. We will then use this result to prove an exact Schur-Horn theorem for (positive)operators with finite spectrum and an approximate Schur-Horn theorem for general (positive)operators.
Rajarama Bhat B. V.
Ravichandran Mohan
No associations
LandOfFree
The Schur-Horn theorem for operators with finite spectrum 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 The Schur-Horn theorem for operators with finite spectrum, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Schur-Horn theorem for operators with finite spectrum will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-68687