Subnormal operators of finite type I. Xia's model and real algebraic curves in C2.

Título inglés Subnormal operators of finite type I. Xia's model and real algebraic curves in C2.
Título español Operadores subnormales de tipo finito I. Modelo de Xia y curvas algebraicas reales en C2.
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
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