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arXiv · 2210.09734

Numerical radius norm and extreme contractions of $L(H)$

Arpita Mal
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Abstract

Suppose $L(H)$ is the space of all bounded linear operators on a complex Hilbert space $H.$ This article deals with the problem of characterizing the extreme contractions of $L(H)$ with respect to the numerical radius norm on $L(H).$ In contrast to the usual operator norm, it is proved that there exists a class of unitary operators on $H$ which are not extreme contractions when the numerical radius norm is considered on $L(H).$ Moreover, there are non-unitary operators on $H$ which are extreme contractions as far as the numerical radius norm is concerned.

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Arpita Mal. 2022-10-18. Numerical radius norm and extreme contractions of $L(H)$. https://arxiv.org/abs/2210.09734

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