Journal of Convex Analysis 29 (2022), No. 2, 371--380
Copyright 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.
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