Proper improvement of well-known numerical radius inequalities and their applications
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| Format: | Preprint |
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2020
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| _version_ | 1866913466033373184 |
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| author | Bhunia, Pintu Paul, Kallol |
| author_facet | Bhunia, Pintu Paul, Kallol |
| contents | New inequalities for the numerical radius of bounded linear operators defined on a complex Hilbert space $\mathcal{H}$ are given. In particular, it is established that if $T$ is a bounded linear operator on a Hilbert space $\mathcal{H}$ then \[ w^2(T)\leq \min_{0\leq α\leq 1} \left \| αT^*T +(1-α)TT^* \right \|,\] where $w(T)$ is the numerical radius of $T.$ The inequalities obtained here are non-trivial improvement of the well-known numerical radius inequalities. As an application we estimate bounds for the zeros of a complex monic polynomial. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2009_03206 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Proper improvement of well-known numerical radius inequalities and their applications Bhunia, Pintu Paul, Kallol Functional Analysis 47A12, 15A60, 26C10 New inequalities for the numerical radius of bounded linear operators defined on a complex Hilbert space $\mathcal{H}$ are given. In particular, it is established that if $T$ is a bounded linear operator on a Hilbert space $\mathcal{H}$ then \[ w^2(T)\leq \min_{0\leq α\leq 1} \left \| αT^*T +(1-α)TT^* \right \|,\] where $w(T)$ is the numerical radius of $T.$ The inequalities obtained here are non-trivial improvement of the well-known numerical radius inequalities. As an application we estimate bounds for the zeros of a complex monic polynomial. |
| title | Proper improvement of well-known numerical radius inequalities and their applications |
| topic | Functional Analysis 47A12, 15A60, 26C10 |
| url | https://arxiv.org/abs/2009.03206 |