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Convex Spectral Functions of Compact Operators, Part II: Lower Semicontinuity and Rearrangement Invariance

Borwein, Jonathan M. and Lewis, Adrian and Zhu, Qiji J. (2001) Convex Spectral Functions of Compact Operators, Part II: Lower Semicontinuity and Rearrangement Invariance. Optimization and Related Topics, 47 . pp. 179-196.

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      Abstract

      It was shown in Part I of this work that the Gateaux differentiability of a convex unitarily invariant function is characterized by that of a similar induced rearrangement invariant function on the corresponding spectral space. A natural question is then whether this is also the case for Fr\'echet differentiability. In this paper we show the answer is positive. Although the result appears very natural, the proof turns out to be quite technically involved.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: convex spectral functions, differentiability, rearrangement invariant functions
      Subjects: 47-xx Operator theory > 47Bxx Special classes of linear operators
      49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 28 Sep 2014 14:06
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/251

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