Article
| Title: | Inequalities involving norm and numeri\nobreak cal radius of Hilbert space operators (English) |
| Author: | Goudarzi, Nasrollah |
| Author: | Heydarbeygi, Zahra |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 65 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 45-52 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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\| \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\| \end{align*} where $R=\max\{t,1-t\}$ and $0\le t\le 1$. (English) |
| Keyword: | bounded linear operator |
| Keyword: | numerical radius |
| Keyword: | operator norm |
| Keyword: | inequality |
| MSC: | 47A12 |
| MSC: | 47A30 |
| MSC: | 47A63 |
| DOI: | 10.14712/1213-7243.2025.006 |
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| Date available: | 2025-04-24T07:47:35Z |
| Last updated: | 2025-04-25 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152943 |
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