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On the semigroups of Fredholm mappings

Published online by Cambridge University Press:  09 April 2009

Sadayuki Yamamuro
Sadayuki Yamamuro
Affiliation:
Department of MathematicsInstitute of Advanced StudiesAustralian National University
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Let E1 and E2 be real Banach spaces and let L(E1) and L(E2) be the Banach algebras of all continuous linear mappings on E1 and E2 respectively. It is a well- known result of M. Eidelheit [1] that L(E1) that L(E2) are isomorphic as rings if and only if E1 and E2 are topologically and algebraically isomorphic. It is easy to see that the essential part of his proof is the following fact.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 3 , May 1972 , pp. 378 - 384
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Eidelheit, M., ‘On isomorphisms of rings of linear operators’, Studia Math. 9 (1940), 97–105.Google Scholar
[2]Magill, K. D. Jr, ‘Automorphisms of the semigroup of all differentiable functions’, Glasgow Math. Journ. 8 (1967), 63–66.Google Scholar
[3]Palais, R., Seminar on the Atiyah-Singer index theorem (Ann. of Math. Studies, no. 57, Princeton, 1965).Google Scholar
[4]Smale, S., ‘An infinite dimensional version of Sard's theorem’, Amer. Journ. Math. 87 (1965), 861–866.Google Scholar
[5]Yamamuro, S., ‘A note on d-ideals in some near-algebras’, Journ. Australian Math. Soc. 7 (1967), 129–134.CrossRefGoogle Scholar
[6]Yamamuro, S., ‘A note on semigroups of mappings on Banach spaces’, Journ. Australian Math. Soc., 9 (1969), 455–464.Google Scholar