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Weak compactness in normed linear spaces

Published online by Cambridge University Press:  09 April 2009

D. G. Tacon
D. G. Tacon
Affiliation:
Australian National UniversityCanberra, ACT
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The notion of weak compactness plays an important role in normed linear space theory. However in many instances norm completeness of the space is an important assumption for obtaining relevant theorems. This note generalises the concept of weak compactness for subsets of normed linear spaces and obtains generalisations of known theorems including that of Eberlein [2]. We use the methods and techniques of “non-standard analysis” in the proofs; several useful non-standard results for normed linear spaces are given.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 1 , July 1972 , pp. 9 - 16
Copyright
Copyright © Australian Mathematical Society 1972

References

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