Improvement of inequalities related to powers of the numerical radius-Reference-Cited by-同舟云学术

Improvement of inequalities related to powers of the numerical radius

Published:2024 Issue:7 Volume:9 Page:19089-19103
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Khatib Yaser¹,Shateyi Stanford²

Affiliation:

1. Department of Mathematics, Farhangian of Bojnourd and Education (and Training) Administration of Bojnourd, Iran

2. Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Abstract

<abstract><p>We presented some improvements of the inequalities involving the numerical radius powers for products and sums of the operators investigated in the Hilbert space. We generalized and improved numerical radius inequalities with a generalization of the mixed Schwarz inequality. Among other things, with the help of a fraction and its power, as well as the introduction of $ \xi $, we provided a very good improvement for the $ \omega^r(E) $, for $ E\in \mathcal{B}(\mathcal{H}_s) $.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference16 articles.

1. J. S. Aujla, F. C. Silva, Weak majorization inequalities and convex functions, Linear Algebra Appl., 369 (2003), 217–233. https://doi.org/10.1016/S0024-3795(02)00720-6

2. S. S. Dragomir, Some inequalities generalizing Kato's and Furuta's results, Filomat, 28 (2014), 179–195. https://doi.org/10.2298/FIL1401179D

3. S. S. Dragomir, On some inequalities for numerical radius of operators in Hilbert spaces, Korean J. Math., 25 (2017), 247–259. https://doi.org/10.11568/kjm.2017.25.2.247

4. M. El-Haddad, F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Ⅱ, Stud. Math., 182 (2007), 133–140. https://doi.org/10.4064/sm182-2-3

5. M. Elin, S. Reich, D. Shoikhet, Numerical range of holomoprhic mappings and applications, Cham: Birkhäuser, 2019. https://doi.org/10.1007/978-3-030-05020-7