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Schauder decompositions in locally convex spaces

Published online by Cambridge University Press:  24 October 2008

N. J. Kalton
N. J. Kalton
Affiliation:
University of Warwick
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Extract

A decomposition of a topological vector space E is a sequence of non-trivial subspaces of E such that each x in E can be expressed uniquely in the form , where yi∈Ei for each i. It follows at once that a basis of E corresponds to the decomposition consisting of the one-dimensional subspaces En = lin{xn}; the theory of bases can therefore be regarded as a special case of the general theory of decompositions, and every property of a decomposition may be naturally denned for a basis.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 377 - 392
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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