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L¹ factorizations, moment problems and invariant subspaces

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Chalendar I., Partington J., Smith R.

Studia Mathematica

2005

tom 167

nr 2

183-194

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.

Ograniczanie wyników

1 Studia Mathematica

1 Chalendar I.

1 Partington J.

1 Smith R.

1 2005

Wyniki wyszukiwania

L¹ factorizations, moment problems and invariant subspaces