On permutations, convex hulls, and normal operators

Sunder, V. S. (1982) On permutations, convex hulls, and normal operators Linear Algebra and its Applications, 48 . pp. 403-411. ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0024-3795(82)90123-9


A spectral characterization is obtained for those normal operators which belong to the convex hull of the unitary orbit of a given normal operator on a finite-dimensional space. This is used to prove the following: if A and B are normal operators on an n-dimensional complex Hilbert space H with eigenvalues given by α1,....,αn and β1,....,βn respectively, and if A-B is also normal, then ||A-B||≤maxσεSn||diag(αkσ(k))|| for any unitarily invariant norm on L(H).

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