This paper concerns a family of weak parallelogram laws for Banach spaces. It is shown that the familiar Lebesgue spaces satisfy a range of these inequalities. Connections are made to basic geometric ideas, such as smoothness, convexity, and Pythagorean-type theorems. The results are applied to the linear prediction of random processes spanning a Banach space. In particular, the weak parallelogram laws furnish coefficient growth estimates, Baxter-type inequalities, and criteria for regularity.

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Copyright © 2015 Springer Netherlands

The definitive version is available at: http://link.springer.com/article/10.1007/s10998-014-0078-4

DOI: 10.1007/s10998-014-0078-4

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