$q$-numerical radius of rank-one operators and the generalized Buzano inequality
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916645781372928 |
|---|---|
| author | Denčić, Dušan Stanković, Hranislav Krstić, Mihailo Damnjanović, Ivan |
| author_facet | Denčić, Dušan Stanković, Hranislav Krstić, Mihailo Damnjanović, Ivan |
| contents | Here, we study the $q$-numerical radius of rank-one operators on a Hilbert space $\mathcal{H}$. More precisely, for $q \in [0,1]$ and $a, b \in \mathcal{H}$, we establish the formula \[ ω_q(a \otimes b) = \frac{1}{2}\left(\|a\|\|b\| + q|\langle a, b \rangle| + \sqrt{1-q^2}\sqrt{\|a\|^2\|b\|^2 - |\langle a, b \rangle|^2}\right), \] which represents a generalization of the well-known formula for the numerical radius of a rank-one operator in a Hilbert space, obtained by setting $q = 1$. As a corollary, we also derive a generalization of the classical Buzano inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $q$-numerical radius of rank-one operators and the generalized Buzano inequality Denčić, Dušan Stanković, Hranislav Krstić, Mihailo Damnjanović, Ivan Functional Analysis 47A12, 47A07, 47B99 Here, we study the $q$-numerical radius of rank-one operators on a Hilbert space $\mathcal{H}$. More precisely, for $q \in [0,1]$ and $a, b \in \mathcal{H}$, we establish the formula \[ ω_q(a \otimes b) = \frac{1}{2}\left(\|a\|\|b\| + q|\langle a, b \rangle| + \sqrt{1-q^2}\sqrt{\|a\|^2\|b\|^2 - |\langle a, b \rangle|^2}\right), \] which represents a generalization of the well-known formula for the numerical radius of a rank-one operator in a Hilbert space, obtained by setting $q = 1$. As a corollary, we also derive a generalization of the classical Buzano inequality. |
| title | $q$-numerical radius of rank-one operators and the generalized Buzano inequality |
| topic | Functional Analysis 47A12, 47A07, 47B99 |
| url | https://arxiv.org/abs/2503.05036 |