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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