Document Type

Article

Publication Date

2013

DOI

10.1016/j.jmaa.2013.02.064

Publication Title

Journal of Mathematical Analysis and Applications

Volume

404

Issue

1

Pages

64-70

Abstract

This paper explores a family of weak parallelogram laws for Banach spaces. Some basic properties of such spaces are obtained. The main result is that a Banach space satisfies a lower weak parallelogram law if and only if its dual satisfies an upper weak parallelogram law, and vice versa. Connections are established between the weak parallelogram laws and the following: subspaces, quotient spaces, Cartesian products, and the Rademacher type and co-type properties.

Comments

Web of Science: "Free full-text from publisher -- Elsevier open archive. "

© 2013 Elsevier Inc. All rights reserved.

Original Publication Citation

Cheng, R., & Harris, C. B. (2013). Duality of the weak parallelogram laws on Banach spaces. Journal of Mathematical Analysis and Applications, 404(1), 64-70. doi:10.1016/j.jmaa.2013.02.064

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