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The Schur-Horn theorem in von Neumann algebras | | Mohan Ravichandran
; | | Date: |
5 Sep 2012 | | Abstract: | A few years ago, Richard Kadison thoroughly analysed the diagonals of
projection operators on Hilbert spaces and asked the following question: Let
$mathcal{A}$ be a masa in a type $II_1$ factor $mathcal{M}$ and let $A in
mathcal{A}$ be a positive contraction. Letting $E$ be the canonical normal
conditional expectation from $mathcal{M}$ to $mathcal{A}$, can one find a
projection $P in mathcal{M}$ so that [E(P) = A?] In a later paper, Kadison
and Arveson, as an extension, conjectured a Schur-Horn theorem in type $II_1$
factors. In this paper, I give a proof of this conjecture of Arveson and
Kadison. I also prove versions of the Schur-Horn theorem for type $II_{infty}$
and type $III$ factors as well as finite von Neumann algebras. | | Source: | arXiv, 1209.0909 | | Services: | Forum | Review | PDF | Favorites | |
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