Convex spectral functions of compact operators, Part II: Lower semicontinuity and rearrangement invariance

J. M. Borwein, A. S. Lewis and Q. J. Zhu

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 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.

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