Inequalities involving norm and numerical radius of Hilbert space operators

Nasrollah Goudarzi; Zahra Heydarbeygi

Commentationes Mathematicae Universitatis Carolinae (2024)

  • Issue: 1, page 45-52
  • ISSN: 0010-2628

Abstract

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This paper presents several numerical radii and norm inequalities for Hilbert space operators. These inequalities improve some earlier related inequalities. For an operator A , we prove that ω 2 ( A ) ≤ ∥ A * A + A A * 2 - 1 2 R ( ( 1 - t ) A * A + t A A * - ( ( 1 - t ) ( A * A ) 1 / 2 + ( A A * ) 1 / 2 ) 2 ) ∥ where R = max { t , 1 - t } and 0 ≤ t ≤ 1 .

How to cite

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Goudarzi, Nasrollah, and Heydarbeygi, Zahra. "Inequalities involving norm and numerical radius of Hilbert space operators." Commentationes Mathematicae Universitatis Carolinae (2024): 45-52. <http://eudml.org/doc/299939>.

@article{Goudarzi2024,
abstract = {This paper presents several numerical radii and norm inequalities for Hilbert space operators. These inequalities improve some earlier related inequalities. For an operator $A$, we prove that \begin\{align*\} \omega ^\{2\}(A)\le & \Big \Vert \frac\{A^\{*\}A+AA^\{*\}\}\{2\} -\frac\{1\}\{2R\}\big (( 1-t)\{\{A\}^\{*\}\}A+tA\{\{A\}^\{*\}\} &-((1-t)(A^\{*\}A)^\{1/2\}+( AA^\{*\})^\{1/2\} )^\{2\} \big ) \Big \Vert \end\{align*\} where $R=\max \lbrace t,1-t\rbrace $ and $0\le t\le 1$.},
author = {Goudarzi, Nasrollah, Heydarbeygi, Zahra},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {bounded linear operator; numerical radius; operator norm; inequality},
language = {eng},
number = {1},
pages = {45-52},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Inequalities involving norm and numerical radius of Hilbert space operators},
url = {http://eudml.org/doc/299939},
year = {2024},
}

TY - JOUR
AU - Goudarzi, Nasrollah
AU - Heydarbeygi, Zahra
TI - Inequalities involving norm and numerical radius of Hilbert space operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2024
PB - Charles University in Prague, Faculty of Mathematics and Physics
IS - 1
SP - 45
EP - 52
AB - This paper presents several numerical radii and norm inequalities for Hilbert space operators. These inequalities improve some earlier related inequalities. For an operator $A$, we prove that \begin{align*} \omega ^{2}(A)\le & \Big \Vert \frac{A^{*}A+AA^{*}}{2} -\frac{1}{2R}\big (( 1-t){{A}^{*}}A+tA{{A}^{*}} &-((1-t)(A^{*}A)^{1/2}+( AA^{*})^{1/2} )^{2} \big ) \Big \Vert \end{align*} where $R=\max \lbrace t,1-t\rbrace $ and $0\le t\le 1$.
LA - eng
KW - bounded linear operator; numerical radius; operator norm; inequality
UR - http://eudml.org/doc/299939
ER -

References

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