Some invariant subspaces for A-contractions and applications

Laurian Suciu

Extracta Mathematicae (2006)

  • Volume: 21, Issue: 3, page 221-247
  • ISSN: 0213-8743

Abstract

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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.

How to cite

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Suciu, Laurian. "Some invariant subspaces for A-contractions and applications." Extracta Mathematicae 21.3 (2006): 221-247. <http://eudml.org/doc/41862>.

@article{Suciu2006,
abstract = {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.},
author = {Suciu, Laurian},
journal = {Extracta Mathematicae},
keywords = {Teoría de operadores; Operadores lineales; Subespacio invariante; Contracción},
language = {eng},
number = {3},
pages = {221-247},
title = {Some invariant subspaces for A-contractions and applications},
url = {http://eudml.org/doc/41862},
volume = {21},
year = {2006},
}

TY - JOUR
AU - Suciu, Laurian
TI - Some invariant subspaces for A-contractions and applications
JO - Extracta Mathematicae
PY - 2006
VL - 21
IS - 3
SP - 221
EP - 247
AB - 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.
LA - eng
KW - Teoría de operadores; Operadores lineales; Subespacio invariante; Contracción
UR - http://eudml.org/doc/41862
ER -

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