Convex spectral functions of compact operators

Title: Convex spectral functions of compact operators
Creator: Borwein, J. M.; Read, J.; Lewis, A. S.
Relation: Journal of Nonlinear and Convex Analysis Vol. 1, Issue 1, p. 17-35
Relation: http://www.ybook.co.jp/online2/jncav1-1.html
Publisher: Yokohama Publishers
Resource Type: journal article
Date: 2000
Description: 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 Calderón 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.
Subject: convexity; eigenvalue; compact operator; unitarily invariant; subdifferential; Fenchel conjugate; spectral function
Identifier: http://hdl.handle.net/1959.13/940638
Identifier: uon:13058
Identifier: ISSN:1345-4773
Language: eng
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