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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