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

  • Jonathan M. Borwein
  • Adrian S. Lewis
  • Qiji J. Zhu
Part of the Applied Optimization book series (APOP, volume 47)


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 Fréchet differentibility. In this paper we show the answer is positive. Although the result appears very natural, the proof turns out to be quite technically involved.

Key words

Convex spectral functions differentiability rearrangement invariant functions 

Mathematics Subject Classification (2000)

49J52 47B10 


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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Jonathan M. Borwein
    • 1
  • Adrian S. Lewis
    • 2
  • Qiji J. Zhu
    • 3
  1. 1.Centre for Experimental and Constructive Mathematics, Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  3. 3.Department of Mathematics and StatisticsWestern Michigan UniversityKalamazooUSA

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