Two aspects of small diameter properties

TL;DR

This paper investigates two geometric aspects of Banach spaces with small diameter properties, focusing on their separability and stability in Kothe Bochner spaces.

Contribution

It demonstrates that BDP, BHP, and BSCSP are separably determined and examines their stability in Kothe Bochner spaces.

Findings

BDP, BHP, and BSCSP are separably determined properties

These properties are stable over Kothe Bochner spaces

Provides new insights into the geometry of Banach spaces

Abstract

In this short note, we study two different geometrical aspects of Banach spaces with small diameter properties, namely the Ball Dentable Property (BDP), Ball Huskable Property (BHP) and Ball Small Combination of slice Property (BSCSP). We show that BDP, BHP and BSCSP are separably determined properties. We also explore the stability of these properties over Kothe Bochner spaces.