
Journal of Convex Analysis 28 (2021), No. 1, 067080 Copyright Heldermann Verlag 2021 On Numerical Radius and Crawford Number Attainment Sets of a Bounded Linear Operator Debmalya Sain Dept. of Mathematics, Indian Institute of Science, Bengaluru 560012, Karnataka, India saindebmalya@gmail.com Arpita Mal Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India arpitamalju@gmail.com Pintu Bhunia Department of Mathematics, Jadavpur University, Kolkata 700032, India pintubhunia5206@gmail.com Kallol Paul Department of Mathematics, Jadavpur University, Kolkata 700032, India kalloldada@gmail.com We completely characterize the Crawford number attainment set and the numerical radius attainment set of a bounded linear operator on a Hilbert space. We study the intersection properties of the corresponding attainment sets of numerical radius, Crawford number, norm, minimum norm of a bounded linear operator defined on a normed space. Our study illustrates the similarities and the differences of the extremal properties of a bounded linear operator on a Hilbert space and a general normed space. Keywords: Numerical radius, Crawford number, norm attainment set, bounded linear operator. MSC: 47A12; 46B20. [ Fulltextpdf (128 KB)] for subscribers only. 