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The path functor and faithful representability of banach lie algebras

Published online by Cambridge University Press:  09 April 2009

W. T. van Est  and
S. Świerczkowski
W. T. van Est
Affiliation:
Rijksuniversiteit, Leiden, Holland.
S. Świerczkowski
Affiliation:
Queen's University, Kingston, Ont., Canada.
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In this note “vector space” will mean “Banach space” unless otherwise specified. Accordingly “Lie algebra” will stand for “Banach Lie algebra”. Morphisms between Lie algebras will be assumed continuous. A Banach algebra B will be always assumed associative, and it will be also viewed as a Lie algebra with product [X, YXY− YX. In particular, the Lie algebra gl(V) of endomorphisms of a vector space V will be equipped with the uniform norm. A morphism of Lie algebras L → gl(V) will b called a representation of L in gl(V). Also, if B is a Banach algebra, a morphism of Lie algebras L → B will be called a representation of L in B. From such one evidently obtains a representation of L in gl(B). A representation will be called faithful if it is injective.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 1 , August 1973 , pp. 54 - 69
Copyright
Copyright © Australian Mathematical Society 1973

References

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