Numerical radius preserving operators on 𝐵(𝐻)

Chan, Jor-Ting

doi:10.1090/S0002-9939-1995-1231293-7

Numerical radius preserving operators on $B(H)$
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by Jor-Ting Chan

Proc. Amer. Math. Soc. 123 (1995), 1437-1439

DOI: https://doi.org/10.1090/S0002-9939-1995-1231293-7

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Abstract:

Let H be a Hilbert space over $\mathbb {C}$ and let $B(H)$ denote the vector space of all bounded linear operators on H. We prove that a linear isomorphism $T:B(H) \to B(H)$ is numerical radius-preserving if and only if it is a multiply of a ${C^ \ast }$-isomorphism by a scalar of modulus one.

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