Annals of Functional Analysis

On reversing of the modified Young inequality

A. Salemi and A. Sheikh Hosseini

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In the present paper, by Haagerup theorem, we show that if $A \in \mathbb{M}_{n}$ is a non scalar strictly positive matrix and $\nu \in (0,1)$ be a real number such that $ \nu \neq \frac{1}{2},$ then there exists $X \in \mathbb{M}_{n}$ such that $$\|A^{\nu}XA^{1-\nu}\| > \| \nu AX + (1- \nu)XA\|.$$

Article information

Ann. Funct. Anal., Volume 5, Number 1 (2014), 70-76.

First available in Project Euclid: 5 February 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
Secondary: 15A42: Inequalities involving eigenvalues and eigenvectors 47A30: Norms (inequalities, more than one norm, etc.)

Young inequality numerical radius spectral norm strictly positive matrix


Salemi, A.; Sheikh Hosseini, A. On reversing of the modified Young inequality. Ann. Funct. Anal. 5 (2014), no. 1, 70--76. doi:10.15352/afa/1391614571.

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