Journal of Convex Analysis 28 (2021), No. 1, 067--080
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.
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