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An Infinite Dimensional Version of the Schur–Horn Convexity Theorem

✍ Scribed by Andreas Neumann

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 877 KB
Volume: 161
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3348

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✦ Synopsis

The Schur Horn Convexity Theorem states that for

where p denotes the projection on the diagonal. In this paper we generalize this result to the setting of arbitrary separable Hilbert spaces. It turns out that the theorem still holds, if we take the l -closure on both sides. We will also give a description of the left-hand side for nondiagonalizable hermitian operators. In the last section we use this result to get an extension theorem for invariant closed convex subsets of the diagonal operators.

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