An extension of Ky Fan's dominance theorem

Rahim Alizadeh; Mohammad B. Asadi

doi:10.15352/bjma/1337014672

2012 An extension of Ky Fan's dominance theorem

Rahim Alizadeh, Mohammad B. Asadi

Banach J. Math. Anal. 6(1): 139-146 (2012). DOI: 10.15352/bjma/1337014672

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 $\mathbb{B}(\mathcal{H})$.

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Rahim Alizadeh and Mohammad B. Asadi "An extension of Ky Fan's dominance theorem," Banach Journal of Mathematical Analysis 6(1), 139-146, (2012). https://doi.org/10.15352/bjma/1337014672

Published: 2012

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