On numerical radius and Crawford number attainment sets of a bounded linear operator

Debmalya Sain, Arpita Mal, Pintu Bhunia, Kallol Paul

备注：: 13 pages

英文摘要：

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.

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