Abstract
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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Cheng, R., Ross, W.T. Weak parallelogram laws on banach spaces and applications to prediction. Period Math Hung 71, 45–58 (2015). https://doi.org/10.1007/s10998-014-0078-4
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DOI: https://doi.org/10.1007/s10998-014-0078-4
Keywords
- Parallelogram law
- Pythagorean theorem
- Uniform convexity
- Best predictor
- Baxter’s inequality
- Purely nondeterministic