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Weak Parallelogram Laws for Banach Spaces

Published online by Cambridge University Press:  20 November 2018

W. L. Bynum
W. L. Bynum*
Affiliation:
College of William and Mary Williamsburg, Virginia 23185, U.S.A.
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It has been shown previously that the Lp(μ) spaces for 1 < p ≤ 2 satisfy a weak parallelogram law, and the same methods can be used to show that the Lp(μ) spaces for 2 ≤ p <∞ satisfy a related weak parallelogram law. This paper obtains several equivalent characterizations of Banach spaces which satisfy one of these two weak parallelogram laws. One such characterization involves the conditions on the moduli of convexity and smoothness analyzed by Lindenstrauss.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 3 , 01 September 1976 , pp. 269 - 275
Copyright
Copyright © Canadian Mathematical Society 1976

References

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