Measures of weak non-compactness in spaces of nuclear operators

Abstract

We show that in the space of nuclear operators from to (where ) the two natural ways of measuring weak non-compactness coincide. We also provide explicit formulas for these measures.

As a consequence the same is proved for preduals of atomic von Neumann algebras.

Keywords

• Measure of weak non-compactness
• Space of nuclear operators
• Space of compact operators
• Predual of an atomic von Neumann algebra