The essential norm of bounded diagonal infinite matrices acting on Banach sequence spaces

Abstract

We calculate the essential norm of bounded diagonal infinite matrices acting on Köthe sequence spaces. As a consequence of our result, we obtain a recent criteria for the compactness of multiplication operator acting on Köthe sequence spaces.

Keywords

• diagonal operators
• banach sequence spaces
• compact operators
• essential norm
• primary: 47b60
• 46b45
• secondary: 46e30
• 46b42