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

Revista Matemática Iberoamericana (1998)

- Volume: 14, Issue: 1, page 95-115
- ISSN: 0213-2230

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topYakubovich, Dmitry V.. "Subnormal operators of finite type I. Xia's model and real algebraic curves in C2.." Revista Matemática Iberoamericana 14.1 (1998): 95-115. <http://eudml.org/doc/39547>.

@article{Yakubovich1998,

abstract = {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.},

author = {Yakubovich, Dmitry V.},

journal = {Revista Matemática Iberoamericana},

keywords = {Operadores lineales; Operadores acotados; Espacios de Hilbert; Curvas algebraicas planas; quadrature Riemann surface; normal part; subnormal; normal extension; finite rank self-commutator; finite type},

language = {eng},

number = {1},

pages = {95-115},

title = {Subnormal operators of finite type I. Xia's model and real algebraic curves in C2.},

url = {http://eudml.org/doc/39547},

volume = {14},

year = {1998},

}

TY - JOUR

AU - Yakubovich, Dmitry V.

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

JO - Revista Matemática Iberoamericana

PY - 1998

VL - 14

IS - 1

SP - 95

EP - 115

AB - 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.

LA - eng

KW - Operadores lineales; Operadores acotados; Espacios de Hilbert; Curvas algebraicas planas; quadrature Riemann surface; normal part; subnormal; normal extension; finite rank self-commutator; finite type

UR - http://eudml.org/doc/39547

ER -

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