Rajarama Bhat, B. V. ; Ravichandran, Mohan (2014) The Schur-Horn theorem for operators with finite spectrum Proceedings of the American Mathematical Society, 142 (10). pp. 3441-3453. ISSN 0002-9939
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Official URL: http://doi.org/10.1090/S0002-9939-2014-12114-9
Related URL: http://dx.doi.org/10.1090/S0002-9939-2014-12114-9
Abstract
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.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Mathematical Society. |
ID Code: | 133702 |
Deposited On: | 30 Dec 2022 04:18 |
Last Modified: | 09 Jan 2023 08:12 |
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