Measures of weak non-compactness in spaces of nuclear operators

Abstract

We show that in the space of nuclear operators from ${\ell }^q(\Lambda )$ to ${\ell }^p(J)$ 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.

19 pages

References in corpus (2)

• Quantification of the reciprocal Dunford-Pettis property
• A quantitative version of James' compactness theorem

Cited by in corpus (3)

• Measures of weak non-compactness in preduals of von Neumann algebras and JBW${}^{\ast }$-triples
• Quantitative Schur property and measures of weak non-compactness
• Representation of measures of noncompactness and its applications related to an initial-value problem in Banach spaces