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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

[1]Abraham, R. and Robin, J., Transversal mappings and flows (Benjamin, 1967).Google Scholar
[2]Bochner, S. and Montgomery, D., ‘Groups of differentiable transformations’, Ann. Math. 45 (1945), 685–694.CrossRefGoogle Scholar
[3]Dieudonné, J., Foundations of modern analysis (Academic Press, New York, 1960)Google Scholar
[4]Dorroh, J. R., ‘Semigroups of non–linear transformation,’ Michigan Math. J., 12 (1965) 317–320.CrossRefGoogle Scholar
[5]Eells, J. Jr, ‘A setting for global analysis’, Bull. Amer. Math. Soc. 72 (1966), 751–807.CrossRefGoogle Scholar
[6]Eidelheit, M., ‘On isomorphisms of rings of linear operators,’ Studia Math. 9 (1950), 97–105.CrossRefGoogle Scholar
[7]Magill, K. D. Jr, ‘Automorphisms of the semigroup of all differentiable functions’, Glasgow Math. J. 8 (1967), 63–66.CrossRefGoogle Scholar
[8]Yamamuro, S., ‘On the semigroup of differentiable mappings,’ J. Australian Math. Soc. 10 (1969), 503–510.CrossRefGoogle Scholar