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On the semigroup of all continuous linear mappings on a Banach space

Published online by Cambridge University Press:  17 April 2009

Sadayuki Yamamuro
Sadayuki Yamamuro
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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It is veil-known that every ring automorphism of the ring of all linear transformations of a real vector space into itself is inner. We shall show that, if this ring is regarded as a semigroup with respect to composition and the dimension of the vector space is not less than 2, every semigroup automorphism is inner.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 2 , April 1971 , pp. 201 - 203
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Eidelheit, M., “On isomorphisms of rings of linear operators”, Studia Math. 9 (1940), 97–105.CrossRefGoogle Scholar