The \(\lambda \)-Function in the Space of Trace Class Operators

  • Antonio M. PeraltaEmail author


Let \(C_1(H)\) denote the space of all trace class operators on an arbitrary complex Hilbert space H. We prove that \(C_1(H)\) satisfies the \(\lambda \)-property, and we determine the form of the \(\lambda \)-function of Aron and Lohman on the closed unit ball of \(C_1(H)\) by showing that
$$\begin{aligned} \lambda (a) = \frac{1 - \Vert a\Vert _1 + 2 \Vert a\Vert _{\infty }}{2}, \end{aligned}$$
for every a in \({C_1(H)}\) with \(\Vert a\Vert _1 \le 1\). This is a non-commutative extension of the formula established by Aron and Lohman for \(\ell _1\).

Mathematics Subject Classification

46B20 46E30 46L70 46L05 47A05 47C10 



The author is partially supported by the Spanish Ministry of Economy and Competitiveness and European Regional Development Fund project no. MTM2014-58984-P and Junta de Andalucía grant FQM375.


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Authors and Affiliations

  1. 1.Departamento de Análisis Matemático, Facultad de CienciasUniversidad de GranadaGranadaSpain

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