3 years ago

The $\lambda $ λ -Function in the Space of Trace Class Operators

Antonio M. Peralta

Abstract

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 \(\ell _1\) .

Publisher URL: https://link.springer.com/article/10.1007/s00009-018-1260-3

DOI: 10.1007/s00009-018-1260-3

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