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Matrices with circular symmetry on their unitary orbits and $ C$-numerical ranges


Authors: Chi-Kwong Li and Nam-Kiu Tsing
Journal: Proc. Amer. Math. Soc. 111 (1991), 19-28
MSC: Primary 15A60; Secondary 47A12, 47C99
DOI: https://doi.org/10.1090/S0002-9939-1991-1041014-5
MathSciNet review: 1041014
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Abstract: We give equivalent characterizations for those $ n \times n$ complex matrices $ A$ whose unitary orbits $ \mathcal{U}(A)$ and $ C$-numerical ranges $ {W_C}(A)$ satisfy $ {e^{i\theta }}\mathcal{U}(A) = \mathcal{U}(A)$ or $ {e^{i\theta }}{W_C}(A) = {W_C}(A)$ for some real $ \theta $ (or for all real $ \theta $). In particular, we show that they are the block-cyclic or block-shift operators. Some of these results are extended to infinite-dimensional Hilbert spaces.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1041014-5
Keywords: $ C$-numerical range, unitary orbit, linear operator
Article copyright: © Copyright 1991 American Mathematical Society

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