Subnormal operators, cyclic vectors and reductivity

Béla Nagy. "Subnormal operators, cyclic vectors and reductivity." Studia Mathematica 216.2 (2013): 97-109. <http://eudml.org/doc/285580>.

@article{BélaNagy2013,
abstract = {Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.},
author = {Béla Nagy},
journal = {Studia Mathematica},
keywords = {subnormal operator; cyclic and -cyclic vectors; reductive operator; generalized Hardy spaces; generated invariant and orthogonally reducing subspaces},
language = {eng},
number = {2},
pages = {97-109},
title = {Subnormal operators, cyclic vectors and reductivity},
url = {http://eudml.org/doc/285580},
volume = {216},
year = {2013},
}

TY - JOUR
AU - Béla Nagy
TI - Subnormal operators, cyclic vectors and reductivity
JO - Studia Mathematica
PY - 2013
VL - 216
IS - 2
SP - 97
EP - 109
AB - Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.
LA - eng
KW - subnormal operator; cyclic and -cyclic vectors; reductive operator; generalized Hardy spaces; generated invariant and orthogonally reducing subspaces
UR - http://eudml.org/doc/285580
ER -