Abstract
We prove that for a separable Hilbert space $\mathcal{H}$ with an orthonormal basis $\{e_i\}_{i=1}^\infty$, the equality $\|\cdot\| =\|\sum_{i=1}^{\infty}s_i(\cdot)e_i\otimes e_i \|$ holds for all unitarily invariant norms on $\mathbb{B}(\mathcal{H})$ and Ky Fan's dominance theorem remains valid on $\mathbb{B}(\mathcal{H})$.
Citation
Rahim Alizadeh. Mohammad B. Asadi. "An extension of Ky Fan's dominance theorem." Banach J. Math. Anal. 6 (1) 139 - 146, 2012. https://doi.org/10.15352/bjma/1337014672
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