On the numerical range of operators on some special Banach spaces
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| Main Authors: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866910561802911744 |
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| author | Mandal, Kalidas Bhanja, Aniket Bag, Santanu Paul, Kallol |
| author_facet | Mandal, Kalidas Bhanja, Aniket Bag, Santanu Paul, Kallol |
| contents | The numerical range of a bounded linear operator on a complex Banach space need not be convex unlike that on a Hilbert space. The aim of this paper is to study operators $T$ on $ \ell^2_p $ for which the numerical range is convex. We also obtain a nice relation between $V(T)$ and $ V(T^t)$ considering $ T \in \mathbb{L} (\ell_p^2) $ and $ T^t \in \mathbb{L} (\ell_q^2) ,$ where $T^t$ denotes the transpose of $T$ and $p$ and $q$ are conjugate real numbers i.e., $ 1 <p,q< \infty $ and $ \frac{1}{p}+\frac{1}{q}=1.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_01288 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the numerical range of operators on some special Banach spaces Mandal, Kalidas Bhanja, Aniket Bag, Santanu Paul, Kallol Functional Analysis Primary 47A12, Secondary 46A55 The numerical range of a bounded linear operator on a complex Banach space need not be convex unlike that on a Hilbert space. The aim of this paper is to study operators $T$ on $ \ell^2_p $ for which the numerical range is convex. We also obtain a nice relation between $V(T)$ and $ V(T^t)$ considering $ T \in \mathbb{L} (\ell_p^2) $ and $ T^t \in \mathbb{L} (\ell_q^2) ,$ where $T^t$ denotes the transpose of $T$ and $p$ and $q$ are conjugate real numbers i.e., $ 1 <p,q< \infty $ and $ \frac{1}{p}+\frac{1}{q}=1.$ |
| title | On the numerical range of operators on some special Banach spaces |
| topic | Functional Analysis Primary 47A12, Secondary 46A55 |
| url | https://arxiv.org/abs/2005.01288 |