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On the semigroups of Fredholm mappings

  • Sadayuki Yamamuro (a1)

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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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References

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[1]Eidelheit, M., ‘On isomorphisms of rings of linear operators’, Studia Math. 9 (1940), 97105.
[2]Magill, K. D. Jr, ‘Automorphisms of the semigroup of all differentiable functions’, Glasgow Math. Journ. 8 (1967), 6366.
[3]Palais, R., Seminar on the Atiyah-Singer index theorem (Ann. of Math. Studies, no. 57, Princeton, 1965).
[4]Smale, S., ‘An infinite dimensional version of Sard's theorem’, Amer. Journ. Math. 87 (1965), 861866.
[5]Yamamuro, S., ‘A note on d-ideals in some near-algebras’, Journ. Australian Math. Soc. 7 (1967), 129134.
[6]Yamamuro, S., ‘A note on semigroups of mappings on Banach spaces’, Journ. Australian Math. Soc., 9 (1969), 455464.
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On the semigroups of Fredholm mappings

  • Sadayuki Yamamuro (a1)

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