Computing Borel complexity of some geometrical properties in Banach spaces

TL;DR

This paper determines the Borel complexity of various classes of Banach spaces with specific geometric properties, providing optimal results that advance the understanding of their classification.

Contribution

It computes the Borel complexity for several Banach space classes, completing previous research and establishing optimality in most cases.

Findings

Borel complexity of diameter two properties calculated

Borel complexity of spaces satisfying the Daugavet equation determined

Borel complexity of spaces with octahedral norms established

Abstract

We compute the Borel complexity of some classes of Banach spaces such as different versions of diameter two properties, spaces satisfying the Daugavet equation or spaces with an octahedral norm. In most of the above cases our computation is even optimal, which completes the research done during the last years around this topic for isomorphism classes of Banach spaces.