Banach spaces of linear operators and homogeneous polynomials without the approximation property

TL;DR

This paper provides numerous examples of Banach spaces of linear operators and homogeneous polynomials lacking the approximation property, advancing previous research in the field.

Contribution

It introduces many new examples of such Banach spaces, improving upon earlier results by Dineen, Mujica, Godefroy, and Saphar.

Findings

Many new examples of Banach spaces without the approximation property.

Improved understanding of the structure of these Banach spaces.

Enhanced classification of spaces lacking the approximation property.

Abstract

We present many examples of Banach spaces of linear operators and homogeneous polynomials without the approximation property, thus improving results of Dineen and Mujica [11] and Godefroy and Saphar [13].