# Stability results of properties related to the Bishop-Phelps-Bollob\'as property for operators

## TL;DR

This paper investigates the stability of the Bishop-Phelps-Bollobás property for operators in Banach spaces, showing stability under finite products with absolute norms and providing optimality examples.

## Contribution

It establishes that the class of Banach spaces with the property is stable under finite products with absolute norms and demonstrates the optimality of previous stability results.

## Key findings

- Stability of the property under finite products with absolute norms.
- Examples confirming the optimality of earlier stability results.

## Abstract

We prove that the class of Banach spaces $Y$ such that the pair $(\ell_1, Y)$ has the Bishop-Phelps-Bollob\'as property for operators is stable under finite products when the norm of the product is given by an absolute norm. We also provide examples showing that previous stability results obtained for that property are optimal.