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Measures of weak non-compactness in spaces of nuclear operators

  • Jan Hamhalter
  • Ondřej F. K. KalendaEmail author
Article
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Abstract

We show that in the space of nuclear operators from \(\ell ^q(\Lambda )\) to \(\ell ^p(J)\) (where \(p,q\in (1,\infty )\)) 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 

Mathematics Subject Classification

46B04 46B50 46B28 46L10 47B10 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Electrical EngineeringCzech Technical University in PraguePrague 6Czech Republic
  2. 2.Department of Mathematical Analysis, Faculty of Mathematics and PhysicsCharles UniversityPrague 8Czech Republic

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