## Banach Journal of Mathematical Analysis

- Banach J. Math. Anal.
- Volume 6, Number 1 (2012), 139-146.

### An extension of Ky Fan's dominance theorem

Rahim Alizadeh and Mohammad B. Asadi

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

#### Article information

**Source**

Banach J. Math. Anal., Volume 6, Number 1 (2012), 139-146.

**Dates**

First available in Project Euclid: 14 May 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.bjma/1337014672

**Digital Object Identifier**

doi:10.15352/bjma/1337014672

**Mathematical Reviews number (MathSciNet)**

MR2862550

**Zentralblatt MATH identifier**

1243.47025

**Subjects**

Primary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

Secondary: 47A30: Norms (inequalities, more than one norm, etc.)

**Keywords**

$s$-numbers, , unitarily invariant norm Ky Fan norm

#### Citation

Alizadeh, Rahim; Asadi, Mohammad B. An extension of Ky Fan's dominance theorem. Banach J. Math. Anal. 6 (2012), no. 1, 139--146. doi:10.15352/bjma/1337014672. https://projecteuclid.org/euclid.bjma/1337014672