Quantitative versions of almost squareness and diameter 2 properties

Authors

  • Eve Oja Institute of Mathematics and Statistics, University of Tartu, 50090 Tartu, Estonia
  • Natalia Saealle Institute of Mathematics and Statistics, University of Tartu, 50090 Tartu, Estonia
  • Indrek Zolk Institute of Mathematics and Statistics, University of Tartu, 50090 Tartu, Estonia https://orcid.org/0000-0003-3230-3877

DOI:

https://doi.org/10.12697/ACUTM.2020.24.09

Keywords:

M-ideal, renorming, almost square, diameter 2 properties

Abstract

We introduce a quantitative version (using s ∈ 2 (0; 1]) of almost (local) squareness of Banach spaces. The latter concept (i.e., the s = 1 case) was introduced by Abrahamsen, Langemets, and Lima in 2016. Related diameter 2 properties (local, strong, and symmetric strong) are also relaxed correspondingly. Our note contains some (counter-)examples and results for the s-almost (local) squareness property.

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Author Biography

Eve Oja, Institute of Mathematics and Statistics, University of Tartu, 50090 Tartu, Estonia

[The author passed away before publication, on 27 January 2019]

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Published

2020-09-23

Issue

Vol. 24 No. 1 (2020)

Section

Articles