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

作者：Wang, Ruofei^*

来源：CHINESE ANNALS OF MATHEMATICS SERIES B, 2023, 44(3): 407-444.

DOI：10.1007/s11401-023-0023-z

• Unitary orbits
• Riesz interpolation property
• Tracial rank one
• D-c(x
• y)

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)) =delta(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)) = D-c(x,y) in unital AT-algebras and in unital simple C*-algebras of tracial rank one, where x, y are self-adjoint elements and D-C (x, y) is a notion generalized from delta(x,y).