On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space
Tóm tắt
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 finite-dimensional Banach space.
Tài liệu tham khảo
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