Convex spectral functions of compact operators, Part 1

Borwein, Jonathan M. and Lewis, Adrian and Read, John and Zhu, Qiji J. (2000) Convex spectral functions of compact operators, Part 1. J. Nonlinear and Convex Analysis, 1 . pp. 17-36.

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      We consider functions on the space of compact self-adjoint Hilbert space operators. Specifically, we study those extended-real functions which depend only on the operators' spectral sequences. Examples include the norms of the Schatten $p$-spaces, the Calder\'on norms, the $k$'th largest eigenvalue, and some infinite-dimensional self-concordant barriers. We show how various convex and nonsmooth-analytic properties of such functions follow from the corresponding properties of the restrictions to the space of diagonal operators, and we derive subdifferential and conjugacy formulas.

      Item Type: Article
      Additional Information: pubdom FALSE
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      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 28 Sep 2014 14:10

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