A Note on an Asymptotic Property of the Convexity of Norms

Authors

  • Petar Evgeniev Sofia University “St. Kliment Ohridski”, Bulgaria

DOI:

https://doi.org/10.7546/CRABS.2025.01.01

Keywords:

asymptotically midpoint uniformly convex spaces, local asymptotic properties

Abstract

We observe that the recently introduced property local asymptotically midpoint uniform convexity (LAMUC}) is isomorphically distinct from AMUC. Specifically, we show that $$c_0$$ or $$T^*$$, with any locally uniformly rotund norm are strictly locally AMUC. We introduce local AUC in the same spirit and give an example of locally AMUC, not locally AUC and not isomorphic to AMUC space. Following the proof in  [10] we observe that these local properties are stable under finite sums with outer space having 1-unconditional basis and uniformly monotone norm.

Author Biography

Petar Evgeniev, Sofia University “St. Kliment Ohridski”, Bulgaria

Mailing Address:
Faculty of Mathematics and Informatics,
Sofia University “St. Kliment Ohridski”,
5, James Bourchier Blvd, 1164 Sofia, Bulgaria

E-mail: psevgeniev@uni-sofia.bg

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Published

29-01-2025

How to Cite

[1]
P. Evgeniev, “A Note on an Asymptotic Property of the Convexity of Norms”, C. R. Acad. Bulg. Sci., vol. 78, no. 1, pp. 3–12, Jan. 2025.

Issue

Section

Mathematics