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An Infinite Dimensional Version of Sard's Theorem

✍ Scribed by S. Smale


Book ID
121741220
Publisher
John Hopkins University Press
Year
1965
Tongue
English
Weight
572 KB
Volume
87
Category
Article
ISSN
0002-9327

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In this paper we generalize the linear Kostant Convexity Theorem to Lie algebras of bounded linear operators on a Hilbert space: If t is a Cartan subspace of one of the hermitian real forms h(H), ho(I c ), hsp(I a ), p t is the projection on t, U the corresponding unitary group and W the correspondi

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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 desc