Numerical Radius Inequalities via Orlicz function
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910574776942592 |
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| author | Bhunia, Pintu Nayak, Raj Kumar |
| author_facet | Bhunia, Pintu Nayak, Raj Kumar |
| contents | Employing the Orlicz functions we extend the Buzano's inequality which is a refinement of the Cauchy-Schwarz inequality. Also using the Orlicz functions
we obtain several numerical radius inequalities for a bounded linear operator as well as the products of operators. We deduce different new upper bounds for the numerical radius. It is shown that \begin{eqnarray*}
{w(T)} \leq \sqrt[n]{ \log \left[ \frac{1}{2^{n-1}} e^{w(T^n)} + \left( 1-\frac{1}{2^{n-1}}\right) e^{\|T\|^n}\right]} &\leq& \|T\| \quad \forall n=2,3,4, \ldots
\end{eqnarray*}
where $w(T)$ and $\|T\|$ denote the numerical radius and the operator norm of a bounded linear operator $T$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical Radius Inequalities via Orlicz function Bhunia, Pintu Nayak, Raj Kumar Functional Analysis 47A12, 47A30, 15A60 Employing the Orlicz functions we extend the Buzano's inequality which is a refinement of the Cauchy-Schwarz inequality. Also using the Orlicz functions we obtain several numerical radius inequalities for a bounded linear operator as well as the products of operators. We deduce different new upper bounds for the numerical radius. It is shown that \begin{eqnarray*} {w(T)} \leq \sqrt[n]{ \log \left[ \frac{1}{2^{n-1}} e^{w(T^n)} + \left( 1-\frac{1}{2^{n-1}}\right) e^{\|T\|^n}\right]} &\leq& \|T\| \quad \forall n=2,3,4, \ldots \end{eqnarray*} where $w(T)$ and $\|T\|$ denote the numerical radius and the operator norm of a bounded linear operator $T$, respectively. |
| title | Numerical Radius Inequalities via Orlicz function |
| topic | Functional Analysis 47A12, 47A30, 15A60 |
| url | https://arxiv.org/abs/2408.12848 |