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arXiv · 2005.01288

On the numerical range of operators on some special Banach spaces

Kalidas Mandal·Aniket Bhanja·Santanu Bag·Kallol Paul
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Abstract

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.$

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Kalidas Mandal, Aniket Bhanja, Santanu Bag, Kallol Paul. 2020-05-04. On the numerical range of operators on some special Banach spaces. https://arxiv.org/abs/2005.01288

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