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

Yakubovich, 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 -