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Periodica Mathematica Hungarica

, Volume 71, Issue 1, pp 45–58 | Cite as

Weak parallelogram laws on banach spaces and applications to prediction

  • R. ChengEmail author
  • W. T. Ross
Article

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.

Keywords

Parallelogram law Pythagorean theorem Uniform convexity Best predictor Baxter’s inequality Purely nondeterministic 

Mathematics Subject Classification

46B20 46B25 60G25 

Notes

Acknowledgments

The authors are grateful to the Referee for his or her helpful comments and suggestions.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsOld Dominion UniversityNorfolkUSA
  2. 2.Department of Mathematics and Computer ScienceUniversity of RichmondRichmondUSA

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