Título inglés |
Subnormal operators of finite type II. Structure theorems. |
Título español |
Operadores sub-normales de tipo finito II. Teoremas de estructura. |
Autor/es |
Yakubovich, Dmitry V. |
Organización |
Div. Math. Anal. Dep. Math. Mech. St. Petersburg State Univ., San Petesburgo, Rusia |
Revista |
0213-2230 |
Publicación |
1998, 14 (3): 623-681, 27 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
This paper concerns pure subnormal operators with finite rank self-commutator, which we call subnormal operators of finite type. We analyze Xia's theory of these operators [21]-[23] and give its alternative exposition. Our exposition is based on the explicit use of a certain algebraic curve in C2, which we call the discriminant curve of a subnormal operator, and the approach of dual analytic similarity models of [26]. We give a complete structure result for subnormal operators of finite type, which corrects and strengthens the formulation that Xia gave in [23]. Xia claimed that each subnormal operator of finite type is unitarily equivalent to the operator of multiplication by z on a weighted vector H2-space over a quadrature Riemann surface (with a finite rank perturbation of the norm). We explain how this formulation can be corrected and show that, conversely, every quadrature Riemann surface gives rise to a family of subnormal operators. We prove that this family is parametrized by the so-called characters. As a departing point of our study, we formulate a kind of scattering scheme for normal operators, which includes Xia's model as a particular case. |
Clasificación UNESCO |
120201 |
Palabras clave español |
Operadores lineales ; Curvas algebraicas ; Operador de rango finito ; Espacios de Hilbert ; Estructuras proyectivas |
Código MathReviews |
MR1681587 |
Código Z-Math |
Zbl 0933.47016 |
Acceso al artículo completo |