ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 15A60, 47A12 Wu, Pei Yuan, National Chiao Tung University, Taiwan Numerical range of S(phi) We study properties of the numerical range W(T) of any completely nonunitary contraction T with rank (1 - T*T) = 1 on a finite-dimensional HIlbert space. We show that such operators are completely characterized by the socalled Poncelet property of their numerical ranges, namely, an n-dimensional contraction T is in the above class if and only if for any point z on the unit circle there is an (n+1)-gon which is inscribed in the unit circle, circumscribed about W(T) and has z as a vertex. We also determine a necessary and sufficient condition on the tangent points in order that the contraction with the above Poncelet property exists. This is a joint work with Hwa-Long Gau.