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On the semigroups of Fredholm mappings
Published online by Cambridge University Press: 09 April 2009
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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.
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- 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
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[6]Yamamuro, S., ‘A note on semigroups of mappings on Banach spaces’, Journ. Australian Math. Soc., 9 (1969), 455–464.Google Scholar
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