Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 29 (2022), No. 2, 371--380Copyright Heldermann Verlag 2022 On the Numerical Range of Operators on some Special Banach Spaces Kalidas Mandal Dept. of Mathematics, Jadavpur University, Kolkata, West Bengal, India kalidas.mandal14@gmail.com Aniket Bhanja Dept. of Mathematics, Vivekananda College Thakurpukur, Kolkata, West Bengal, India aniketbhanja219@gmail.com Santanu Bag Dept. of Mathematics, Vivekananda College for Women, Barisha, Kolkata, West Bengal, India santanumath84@gmail.com Kallol Paul Dept. of Mathematics, Jadavpur University, Kolkata, West Bengal, India kalloldada@gmail.com [Abstract-pdf] 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 Keywords: Semi-inner-product, numerical range, convex set. MSC: 47A12; 46A55. [ Fulltext-pdf  (121  KB)] for subscribers only.