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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Numerical radius preserving operators on $B(H)$
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by Jor-Ting Chan PDF
Proc. Amer. Math. Soc. 123 (1995), 1437-1439 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1437-1439
  • MSC: Primary 47A12; Secondary 47B49
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1231293-7
  • MathSciNet review: 1231293