NEW CLASSES OF HYPERCYCLIC TOEPLITZ OPERATORS

Evgeny Abakumov (1) , Anton Baranov (2) , Stéphane Charpentier (3) , Andrei Lishanskii (2)

1 LAMA - Laboratoire Analyse et Mathématiques Appliquées
2 SPbU - St Petersburg State University
3 I2M - Institut de Mathématiques de Marseille

We study hypercyclicity of Toeplitz operators in the Hardy space H 2 (D) with symbols of the form R(z) + ϕ(z), where R is a rational function and ϕ ∈ H ∞ (D). We relate this problem to cyclicity of certain families of functions for analytic Toeplitz operators and give new sufficient conditions for hypercyclicity based on deep results of B. Solomyak.

Keywords: 47A16; 47B35; 30H10; Toeplitz operator; univalent function; hypercyclic operator

Domains: Mathematics [math]; Functional Analysis [math.FA]

Evgeny Abakumov, Anton Baranov, Stéphane Charpentier, Andrei Lishanskii. NEW CLASSES OF HYPERCYCLIC TOEPLITZ OPERATORS. Bulletin des Sciences Mathématiques, 2021, 168, pp.102971. ⟨10.1016/j.bulsci.2021.102971⟩. ⟨hal-03466292⟩