Annals of Functional Analysis

On reversing of the modified Young inequality

A. Salemi and A. Sheikh Hosseini

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 5 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1391614571

Digital Object Identifier
doi:10.15352/afa/1391614571

Mathematical Reviews number (MathSciNet)
MR3119114

Zentralblatt MATH identifier
1280.15013

Subjects
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.)

Keywords
Young inequality numerical radius spectral norm strictly positive matrix

Citation

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. https://projecteuclid.org/euclid.afa/1391614571


Export citation

References

  • T. Ando, Majorization and inequalities in matrix theory, Linear Algebra Appl. 199 (1994), 17–67.
  • T. Ando, Matrix Young inequalities, Oper. Theory Adv. Appl. 75 (1995), 33–38.
  • T. Ando, R.A. Horn and C.R. Johnson, The singular values of a Hadamard product: A basic inequality, Linear Multilinear Algebra 21 (1987), 345–365.
  • T. Ando and K. Okubo, Induced norms of the Schur multiplication operators, Linear Algebra Appl. 147(1991), 181–199.
  • R. Bhatia, Positive Definite Matrices, Princeton University Press, 2007.
  • R. Bhatia and C. Davis, More matrix forms of the arithmetic-geometric mean inequality, SIAM J. Matrix Anal. Appl. 14(1993), 132–136.
  • R. Bhatia and F. Kittaneh, On the singular values of a product of operators, SIAM J. Matrix Anal. Appl. 11 (1990), 272–277.
  • C. Conde, Young type inequalities for positive operators, Ann. Funct. Anal. 2 (2013), no. 2, 144–152.
  • A. Salemi and A. Sheikh Hosseini, Matrix Young numerical radius inequalities, Math. Inequal. Appl. 16 (2013), no. 3, 783–791.
  • A. Salemi and A. Sheikh Hosseini, Numerical radius and operator norm inequalities, preprint.
  • X. Zhan, Inequalities for unitarily invariant norms, SIAM J. Matrix Anal. Appl. 20 (1998) 466–470.
  • X. Zhan, Matrix Inequalities(Lecture notes in mathematics), 1790, Springer, 2002.