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On the semigroup of Hadamard differentiable mappings

  • Sadayuki Yamamuro (a1)

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The main purpose of this paper is to prove that every automorphism of the semigroup of all Hadamard-differentiable mappings of a separable real Banach space into itself is inner. This generalizes the results of [7] which is a generalization of a result proved by Magill, Jr. [5].

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References

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[1]Averbukh, V. I. and Smolyanov, O. G., ‘The theory of differentiation in linear topological spaces,’ Russian Math. Survey, 22: 6 (1967), 201258.
[2]Averbukh, V. I. and Smolyanov, O. G., ‘The various definitions of the derivative in linear topological spaces,’ Russian Math. Survey, 23: 4 (1968), 67113.
[3]Dieudonné, J., Foundations of Modern Analysis (1960).
[4]Eidelheit, M., ‘On isomorphisms of rings of linear operators.’ Studia M. 9 (1940), 97105.
[5]Magill, K. D. Jr, ‘Automorphisms of the semigroup of all differentiable functions,’ Glasgow Math. J. 8 (1967), 6366.
[6]Schwartz, J. T., Non-linear Functional Analysis (Gordon and Breach, New York, 1969).
[7]Wood, G. R. and Yamamuro, Sadayuki, ‘On the semigroup of differentiable mappings’ (II); (to appear in Glasgow Math. J.).
[8]Yamamuro, Sadayuki, ‘On the semigroup of differentiable mappings,’ J. Australian Math. Soc. 10 (1969), 503510.
[9]Yamamuro, Sadayuki, ‘On the semigroup of bounded C 1-mappings,’ (to appear in J. Australian Math. Soc.)
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On the semigroup of Hadamard differentiable mappings

  • Sadayuki Yamamuro (a1)

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