On the zero set of the Kobayashi–Royden pseudometric of the spectral unit ball

Tom 93 / 2008

Nikolai Nikolov, Pascal J. Thomas Annales Polonici Mathematici 93 (2008), 53-68 MSC: Primary 32F45; Secondary 32A07. DOI: 10.4064/ap93-1-4

Streszczenie

Given $A\in {\mit\Omega} _n,$ the $n^2$-dimensional spectral unit ball, we show that if $B$ is an $n\times n$ complex matrix, then $B$ is a “generalized” tangent vector at $A$ to an entire curve in ${\mit\Omega} _n$ if and only if $B$ is in the tangent cone $C_A$ to the isospectral variety at $A.$ In the case of ${\mit\Omega} _3,$ the zero set of the Kobayashi–Royden pseudometric is completely described.

Autorzy

  • Nikolai NikolovInstitute of Mathematics and Informatics
    Bulgarian Academy of Sciences
    Acad. G. Bonchev 8
    1113 Sofia, Bulgaria
    e-mail
  • Pascal J. ThomasLaboratoire Émile Picard
    UMR CNRS 5580
    Université Paul Sabatier
    118 Route de Narbonne
    F-31062 Toulouse Cedex, France
    e-mail

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