Discontinuity of the Lempert function of the spectral ball

Pascal J. Thomas (1) , Nguyen van Trao (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 DHSP - Laboratory of Complex Geometry

We give some further criteria for continuity or discontinuity of the Lempert funtion of the spectral ball $\Omega_n$, with respect to one or both of its arguments, in terms of cyclicity the matrices involved.

Mots clés: Lempert function; spectral ball; cyclic matrices

Domaines: Variables complexes [math.CV]

Pascal J. Thomas, Nguyen van Trao. Discontinuity of the Lempert function of the spectral ball. Proceedings of the American Mathematical Society, 2010, 138 (7), pp.2403-2412. ⟨10.1090/S0002-9939-10-10269-X⟩. ⟨hal-00345717⟩