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On Fréchet differentiability of convex functions on Banach spaces. (English) Zbl 0831.46045
Summary: Equivalent conditions for the separability of the range of the subdifferential of a given convex Lipschitz function \(f\) defined on a separable Banach space are studied. The conditions are in terms of a majorization of \(f\) by a \(C^1\)-smooth function, separability of the boundary for \(f\) or an approximation of \(f\) by Fréchet smooth convex functions.

MSC:
46G05 Derivatives of functions in infinite-dimensional spaces
49J50 Fréchet and Gateaux differentiability in optimization
46B03 Isomorphic theory (including renorming) of Banach spaces
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