The Schur-Horn Convexity Theorem states that for a in R~n p({U~* diag(a) U:U implied by U(n)})=conv (G_na), 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~(infinity)-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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机译：舒尔-霍恩凸定理指出，对于R in n p（{U〜* diag（a）U：U，U（n）}）= conv（G_na），其中p表示对角线上的投影。在本文中，我们将此结果推广到任意可分离的希尔伯特空间的设置。事实证明，如果我们在两边都取l〜（无穷大）闭包，则该定理仍然成立。我们还将对不可对角化的厄米算子进行左侧描述。在最后一节中，我们使用此结果获得对角算子的不变封闭凸集的扩展定理。
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