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arXiv · 2006.15323

On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space

Pintu Bhunia·Debmalya Sain·Kallol Paul
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Abstract

We study the Davis-Wielandt shell and the Davis-Wielandt radius of an operator on a normed linear space $\mathcal{X}$. We show that after a suitable modification, the modified Davis-Wielandt radius defines a norm on $\mathcal{L}(\mathcal{X})$ which is equivalent to the usual operator norm on $\mathcal{L}(\mathcal{X})$. We introduce the Davis-Wielandt index of a normed linear space and compute its value explicitly in case of some particular polyhedral Banach spaces. We also present a general method to estimate the Davis-Wielandt index of any polyhedral Banach space.

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Pintu Bhunia, Debmalya Sain, Kallol Paul. 2020-06-27. On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space. https://doi.org/10.1007/s13348-021-00332-7

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