Some invariant subspaces for the operators A and T acting on a Hilbert space H and satisfying T*AT ≤ A and A ≥ 0, are presented. Especially, the largest invariant subspace for A and T on which the equality T* AT = A occurs, is studied in connections to others invariant or reducing subspaces for A, or T. Such subspaces are related to the asymptotic form of the subspace quoted above, this form being obtained using the operator limit of the sequence {T*nATn; n ≥ 1}. More complete results are given in the case when AT = A1/2TA1/2. Also, several applications for quasinormal operators are derived, involving their unitary, isometric and quasi-isometric parts, as well as their asymptotic behaviour.
@article{urn:eudml:doc:41862,
title = {Some invariant subspaces for A-contractions and applications},
journal = {Extracta Mathematicae},
volume = {21},
year = {2006},
pages = {221-247},
zbl = {1179.47006},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41862}
}
Suciu, Laurian. Some invariant subspaces for A-contractions and applications. Extracta Mathematicae, Tome 21 (2006) pp. 221-247. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41862/