The Lipschitz bounded approximation property for operator ideals

TL;DR

This paper introduces the Lipschitz bounded approximation property for operator ideals, extending prior work and exploring its relation to the bounded approximation property and three space problems.

Contribution

It defines a new Lipschitz bounded approximation property for operator ideals and investigates its connections and implications in approximation theory.

Findings

Extended Godefroy and Kalton's work on approximation properties

Provided partial answers on equivalence between properties

Analyzed three space problems related to these properties

Abstract

In this article, we introduce the Lipschitz bounded approximation property for operator ideals. With this notion, we extend the original work done by Godefroy and Kalton and give some partial answers on the equivalence between the bounded approximation property and the Lipschitz bounded approximation property based on an arbitrary operator ideal. Furthermore, we investigate the three space problems on the preceding bounded approximation properties.