Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591096 | Journal of Functional Analysis | 2010 | 48 Pages |
Abstract
The main result of this paper is the extension of the Schur–Horn Theorem to infinite sequences: For two nonincreasing nonsummable sequences ξ and η that converge to 0, there exists a positive compact operator A with eigenvalue list η and diagonal sequence ξ if and only if for every n if and only if ξ=Qη for some orthostochastic matrix Q. When ξ and η are summable, requiring additionally equality of their infinite series obtains the same conclusion, extending a theorem by Arveson and Kadison. Our proof depends on the construction and analysis of an infinite product of T-transform matrices.
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