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On the semigroup of bounded C1-mappings
Published online by Cambridge University Press: 09 April 2009
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Let E be a real Banach space. If f: E→E is (Fréchet-) differentiable at every point of E, the derivative of f at x is denoted by f'(x), which is an element of the Banach algebra ℒ=ℒ(E) of all linear continuous mappings of E into itself with the usual upper bound norm, and, if we put , we have .
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- Copyright © Australian Mathematical Society 1973