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Distance Between Unitary Orbits of Self-Adjoint Elements in C*-Algebras of Tracial Rank One

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Abstract

The note studies certain distance between unitary orbits. A result about Riesz interpolation property is proved in the first place. Weyl (1912) shows that dist(U(x), U(y)) =δ(x,y) for self-adjoint elements in matrixes. The author generalizes the result to C*-algebras of tracial rank one. It is proved that dist(U(x),U(y)) = Dc(x,y) in unital AT-algebras and in unital simple C*-algebras of tracial rank one, where x, y are self-adjoint elements and DC (x, y) is a notion generalized from δ(x,y).

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Acknowledgements

The author wishes to thank his doctoral supervisor Lin for guidance. He also wishes to thank professor Hu and doctor Liu for help.

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Authors and Affiliations

  1. Department of Mathematics and the Research Center for Operator Algebras, East China Normal University, Shanghai, 200062, China

    Ruofei Wang

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  1. Ruofei Wang
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Correspondence to Ruofei Wang.

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Wang, R. Distance Between Unitary Orbits of Self-Adjoint Elements in C*-Algebras of Tracial Rank One. Chin. Ann. Math. Ser. B 44, 407–444 (2023). https://doi.org/10.1007/s11401-023-0023-z

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  • DOI: https://doi.org/10.1007/s11401-023-0023-z

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