Symmetric seminorms and the Leibniz property

Zoltan Leka

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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 languageEnglish
Pages (from-to)708-725
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume452
Issue number1
Early online date14 Mar 2017
DOIs
Publication statusPublished - 1 Aug 2017

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