Título inglés |
Subnormal operators of finite type I. Xia's model and real algebraic curves in C^{2}. |

Título español |
Operadores subnormales de tipo finito I. Modelo de Xia y curvas algebraicas reales en C^{2}. |

Autor/es |
Yakubovich, Dmitry V. |

Organización |
Div. Math. Anal. Dep. Math. Mech. Saint Petersburg State Univ., San Petersburgo, Rusia |

Revista |
0213-2230 |

Publicación |
1998, 14 (1): 95-115, 13 Ref. |

Tipo de documento |
articulo |

Idioma |
Inglés |

Resumen inglés |
Xia proves in [9] that a pure subnormal operator S is completely determined by its self-commutator C = S*S - SS*, restricted to the closure M of its range and the operator Λ = (S*|M)*. In [9], [10], [11] he constructs a model for S that involves this two operators and the so-called mosaic, which is a projection-valued function, analytic outside the spectrum of the minimal normal extension of S. He finds all pure subnormals S with rank C = 2. We will give a complete description of pairs of matrices (C,Λ) that correspond to some S for the case of the self-commutator C of arbitrary finite rank. It is given in terms of a topological property of a certain algebraic curve, associated with C and Λ. We also give a new explicit formula for Xia's mosaic. |

Clasificación UNESCO |
120201 |

Palabras clave español |
Operadores lineales ; Operadores acotados ; Espacios de Hilbert ; Curvas algebraicas planas |

Código MathReviews |
MR1639287 |

Código Z-Math |
Zbl 0933.47016 |

**Acceso al artículo completo** |