History, Developments and Open Problems on Approximation Properties

Abstract

In this paper, we give a comprehensive review of the classical approximation property. Then, we present some important results on modern variants, such as the weak bounded approximation property, the strong approximation property and p-approximation property. Most recent progress on E-approximation property and open problems are discussed at the end.

Keywords

• Banach space
• unconditional basis
• approximation property