Positivity principle for measures on uniformly convex Banach spaces
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E. A. Riss
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 33 (2022), 687-696
- DOI: https://doi.org/10.1090/spmj/1722
- Published electronically: June 27, 2022
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Abstract:
A Banach space $X$ is said to satisfy the positivity principle for small balls if for every finite Borel measures $\mu$ and $\nu$ on $X$, the inequalities $\mu (B) \leq \nu (B)$ for all balls B of radius less than 1 imply that $\mu \leq \nu$. It is shown that no uniformly convex infinite-dimensional separable Banach space $X$ obeys the positivity principle for small balls.References
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Bibliographic Information
- E. A. Riss
- Affiliation: Department of Mathematics, A. I. Gertsen Russian State Pedagogical University, St. Petersburg, Russia
- Email: e.riss@bk.ru
- Received by editor(s): February 28, 2020
- Published electronically: June 27, 2022
- © Copyright 2022 American Mathematical Society
- Journal: St. Petersburg Math. J. 33 (2022), 687-696
- MSC (2020): Primary 28C20
- DOI: https://doi.org/10.1090/spmj/1722
Dedicated: To the radiant memory of Alexander Isaakovich Plotkin, Dear Teacher