On the Composition of Differentiable Functions
2003 ◽
Vol 46
(4)
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pp. 481-494
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AbstractWe prove that a Banach space X has the Schur property if and only if every X-valued weakly differentiable function is Fréchet differentiable. We give a general result on the Fréchet differentiability of f ○ T, where f is a Lipschitz function and T is a compact linear operator. Finally we study, using in particular a smooth variational principle, the differentiability of the semi norm ‖ ‖lip on various spaces of Lipschitz functions.
1974 ◽
Vol 11
(2)
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pp. 161-166
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2009 ◽
Vol 79
(2)
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pp. 309-317
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1991 ◽
Vol 14
(3)
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pp. 611-614
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2010 ◽
Vol 148
(3)
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pp. 519-529
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1986 ◽
Vol 9
(3)
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pp. 583-587
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