Quantitative versions of almost squareness and 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.