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Measures of weak non-compactness in spaces of nuclear operators

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27, Prague 6, Czech Republic

    Jan Hamhalter

  2. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 86, 186 75, Prague 8, Czech Republic

    Ondřej F. K. Kalenda

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  1. Jan Hamhalter
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  2. Ondřej F. K. Kalenda
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Correspondence to Ondřej F. K. Kalenda.

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Our research was supported in part by the Grant GAČR 17-00941S.

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Hamhalter, J., Kalenda, O.F.K. Measures of weak non-compactness in spaces of nuclear operators. Math. Z. 292, 453–471 (2019). https://doi.org/10.1007/s00209-019-02264-2

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