Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T01:38:37.393Z Has data issue: false hasContentIssue false
  • English
  • Français

On the semigroup of Hadamard differentiable 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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 3 , November 1972 , pp. 329 - 334
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Averbukh, V. I. and Smolyanov, O. G., ‘The theory of differentiation in linear topological spaces,’ Russian Math. Survey, 22: 6 (1967), 201–258.CrossRefGoogle Scholar
[2]Averbukh, V. I. and Smolyanov, O. G., ‘The various definitions of the derivative in linear topological spaces,’ Russian Math. Survey, 23: 4 (1968), 67–113.CrossRefGoogle Scholar
[3]Dieudonné, J., Foundations of Modern Analysis (1960).Google Scholar
[4]Eidelheit, M., ‘On isomorphisms of rings of linear operators.’ Studia M. 9 (1940), 97–105.CrossRefGoogle Scholar
[5]Magill, K. D. Jr, ‘Automorphisms of the semigroup of all differentiable functions,’ Glasgow Math. J. 8 (1967), 63–66.CrossRefGoogle Scholar
[6]Schwartz, J. T., Non-linear Functional Analysis (Gordon and Breach, New York, 1969).Google Scholar
[7]Wood, G. R. and Yamamuro, Sadayuki, ‘On the semigroup of differentiable mappings’ (II); (to appear in Glasgow Math. J.).Google Scholar
[8]Yamamuro, Sadayuki, ‘On the semigroup of differentiable mappings,’ J. Australian Math. Soc. 10 (1969), 503–510.CrossRefGoogle Scholar
[9]Yamamuro, Sadayuki, ‘On the semigroup of bounded C 1-mappings,’ (to appear in J. Australian Math. Soc.)Google Scholar