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 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.
Research was supported by NSERC and by the Shrum Endowment at Simon Fraser University.
Research was supported by NSERC.
Research was supported by the National Science Foundation under grant DMS-9704203.
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Borwein, J.M., Lewis, A.S., Zhu, Q.J. (2001). Convex Spectral Functions of Compact Operators, Part II: Lower Semicontinuity and Rearrangement Invariance. In: Rubinov, A., Glover, B. (eds) Optimization and Related Topics. Applied Optimization, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6099-6_12
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DOI: https://doi.org/10.1007/978-1-4757-6099-6_12
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