L¹ factorizations, moment problems and invariant subspaces

Isabelle Chalendar, Jonathan R. Partington, and Rachael C. Smith. "L¹ factorizations, moment problems and invariant subspaces." Studia Mathematica 167.2 (2005): 183-194. <http://eudml.org/doc/284905>.

@article{IsabelleChalendar2005,
abstract = {For an absolutely continuous contraction T on a Hilbert space 𝓗, it is shown that the factorization of various classes of L¹ functions f by vectors x and y in 𝓗, in the sense that ⟨Tⁿx,y⟩ = f̂(-n) for n ≥ 0, implies the existence of invariant subspaces for T, or in some cases for rational functions of T. One of the main tools employed is the operator-valued Poisson kernel. Finally, a link is established between L¹ factorizations and the moment sequences studied in the Atzmon-Godefroy method, from which further results on invariant subspaces are derived.},
author = {Isabelle Chalendar, Jonathan R. Partington, Rachael C. Smith},
journal = {Studia Mathematica},
keywords = {invariant subspace; operator-valued Poisson kernel; moment sequence; absolutely continuous contraction},
language = {eng},
number = {2},
pages = {183-194},
title = {L¹ factorizations, moment problems and invariant subspaces},
url = {http://eudml.org/doc/284905},
volume = {167},
year = {2005},
}

TY - JOUR
AU - Isabelle Chalendar
AU - Jonathan R. Partington
AU - Rachael C. Smith
TI - L¹ factorizations, moment problems and invariant subspaces
JO - Studia Mathematica
PY - 2005
VL - 167
IS - 2
SP - 183
EP - 194
AB - For an absolutely continuous contraction T on a Hilbert space 𝓗, it is shown that the factorization of various classes of L¹ functions f by vectors x and y in 𝓗, in the sense that ⟨Tⁿx,y⟩ = f̂(-n) for n ≥ 0, implies the existence of invariant subspaces for T, or in some cases for rational functions of T. One of the main tools employed is the operator-valued Poisson kernel. Finally, a link is established between L¹ factorizations and the moment sequences studied in the Atzmon-Godefroy method, from which further results on invariant subspaces are derived.
LA - eng
KW - invariant subspace; operator-valued Poisson kernel; moment sequence; absolutely continuous contraction
UR - http://eudml.org/doc/284905
ER -