Symmetric seminorms and the Leibniz property

Zoltan Leka

doi:10.1016/j.jmaa.2017.02.070

Symmetric seminorms and the Leibniz property

Zoltan Leka

Department of Mathematics

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Abstract

We show that certain symmetric seminorms on Rn satisfy the Leibniz inequality. As an application, we obtain that Lp norms of centered bounded real functions, defined on probability spaces, have the same property. Even though this is well-known for the standard deviation it seems that the complete result has never been established. In addition, we shall connect the results with the differential calculus introduced by Cipriani and Sauvageot and Rieffel's non-commutative Riemann metric.

Original language	English
Pages (from-to)	708-725
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	452
Issue number	1
Early online date	14 Mar 2017
DOIs	https://doi.org/10.1016/j.jmaa.2017.02.070
Publication status	Published - 1 Aug 2017

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10.1016/j.jmaa.2017.02.070Licence: CC BY-NC-ND

Accepted ManuscriptAccepted author manuscript, 335 KBLicence: CC BY-NC-ND

Cite this

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abstract = "We show that certain symmetric seminorms on Rn satisfy the Leibniz inequality. As an application, we obtain that Lp norms of centered bounded real functions, defined on probability spaces, have the same property. Even though this is well-known for the standard deviation it seems that the complete result has never been established. In addition, we shall connect the results with the differential calculus introduced by Cipriani and Sauvageot and Rieffel's non-commutative Riemann metric.",

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