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On the semigroup of bounded C1-mappings

Published online by Cambridge University Press:  09 April 2009

Sadayuki Yamamuro
Sadayuki Yamamuro
Affiliation:
Department of Mathematics Institute of Advanced Studies Australian National University Canberra, A.C.T., 2600
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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 .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 2 , March 1973 , pp. 129 - 137
Copyright
Copyright © Australian Mathematical Society 1973

References

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