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On the semigroup of differentiable mappings (II)

Published online by Cambridge University Press:  18 May 2009

G. R. Wood  and
Sadayuki Yamamuro
G. R. Wood
Affiliation:
Institute of Advanced Studies, Australian National University, Canberra
Sadayuki Yamamuro
Affiliation:
Institute of Advanced Studies, Australian National University, Canberra
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In [2], K. D. Magill, Jr. has proved that every automorphism of the semigroup (with respect to composition) of all real-valued differentiable functions of a real variable is inner. The purpose of this paper is to generalize this fact to arbitrary finite-dimensional real Banach spaces.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 2 , September 1972 , pp. 122 - 128
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Banach, S., Théorie des opérations linéaires (Warsaw, 1932).Google Scholar
2.Magill, K. D. Jr, Automorphisms of the semigroup of all differentiable functions, Glasgow Math. J. 8 (1967), 63–66.CrossRefGoogle Scholar
3.Saks, S., Theory of the integral (New York, 1937).Google Scholar
4.Yamamuro, S., A note on semigroups of mappings on Banach spaces, J. Australian Math. Soc. 9 (1969), 455–464.CrossRefGoogle Scholar
5.Yamamuro, S., On the semigroup of differentiable mappings, J. Australian Math. Soc. 10 (1969), 503–510.CrossRefGoogle Scholar