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A Note on Semigroups of Mappings on Banach Spaces

Published online by Cambridge University Press:  09 April 2009

Sadayuki Yamamuro
Sadayuki Yamamuro
Affiliation:
Department of Mathematics Institute of Advanced Studies Australian National UniversityCanberra
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In a series of papers K. D. Magill, Jr. (see [1] and its references) has proved that, in various semigroups of mappings on topological spaces, every automorphism is inner, where an automorphism φ of a semigroup A is a bijection of A such that for all ƒ and g in A, and it is said to be inner if there exists a bijection h ∈ A such that h−1 (the inverse of h) belongs to A and for every ƒ ∈ A.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 3-4 , May 1969 , pp. 455 - 464
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Browder, F. E., ‘The solvability of non-linear functional equations’, Duke Math. Journ. 30 (1963), 557–566.CrossRefGoogle Scholar
[2]Magill, K. D. Jr, ‘Semigroup structures for families of functions’, Journ. Australian Math. Soc. 7 (1967), 81–107.CrossRefGoogle Scholar
[3]Magill, K. D. Jr, ‘Automorphisms of the semigroup of all differentiable functions’, Glasgow Math. Journ. 8 (1967), 63–66.CrossRefGoogle Scholar
[4]Minty, G. J., ‘Monotone (non-linear) operators in Hilbert spaces’, Duke Math. Journ. 29 (1962), 341–346.CrossRefGoogle Scholar
[5]Rickart, C. E., Banach Algebras, (Van Nostrand).Google Scholar
[6]Yamamuro, S., ‘A note on d-ideals in some near-algebras’, Journ. Australian Math. Soc. 7 (1967), 129–134.CrossRefGoogle Scholar