L¹ factorizations, moment problems and invariant subspaces

• Autorzy: Isabelle Chalendar , Jonathan R. Partington , Rachael C. Smith
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A57: Operator methods in interpolation, moment and extension problems
• 47A15: Invariant subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 167
• Numer: 2
• Strony: 183-194

Daty

wydano

2005

Twórcy

autor

Isabelle Chalendar

• Institut Girard Desargues, UFR de Mathématiques, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France

autor

Jonathan R. Partington

• School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K.

autor

Rachael C. Smith

• School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K.

Identyfikatory

DOI

10.4064/sm167-2-5