Do some nontrivial closed z-invariant subspaces have the division property ?
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Document de travail - Pré-publication
Resumen en inglés
We consider Banach spaces E of functions holomorphic on the open unit disc D such that the unilateral shift S and the backward shift T are bounded on E. Assuming that the spectra of S and T are equal to the closed unit ...Leer más >
We consider Banach spaces E of functions holomorphic on the open unit disc D such that the unilateral shift S and the backward shift T are bounded on E. Assuming that the spectra of S and T are equal to the closed unit disc we discuss the existence of closed z-invariant of N of E having the "division property", which means that the function f λ : z → f (z)/ z−λ belongs to N for every λ ∈ D and for every f ∈ N such that f (λ) = 0. This question is related to the existence of nontrivial bi-invariant subspaces of Banach spaces of hyperfunctions on the unit circle T.< Leer menos
Palabras clave en inglés
AMS Classification : Primary 30B40
47A15
Secondary 30B60
47A68
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