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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-2-1,
author = {B\'ela Nagy},
title = {Subnormal operators, cyclic vectors and reductivity},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {97-109},
zbl = {1305.47018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-2-1}
}
Béla Nagy. Subnormal operators, cyclic vectors and reductivity. Studia Mathematica, Tome 215 (2013) pp. 97-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm216-2-1/