Some characterizations for composition operators on the Fock spaces

Jiang, Liangying; Prǎjiturǎ, Gabriel T.; Zhao, Ruhan

doi:10.1016/j.jmaa.2017.06.023

Cited by 14 publications

(9 citation statements)

References 19 publications

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“…On the classical Fock space, these results were proved recently in [11]. Our result now shows that these properties are independent of the fast growth of the inducing weight function ϕ.…”

Section: Essential Norms and Schatten Class Membershipsupporting

confidence: 69%

“…(ii) can not be supercylic on F p ϕ . The cyclicity and supercyclicity problems have not been solved in the classical Fock spaces settings either except for the Hilbert space case which were studied respectively in [9] and [11]. As can be seen in Section 4, our approach, which neither uses Hilbert spaces techniques nor the fast growth property of the weight function ϕ, shows that the same result holds for all p on the classical spaces as well.…”

Section: Essential Norms and Schatten Class Membershipmentioning

confidence: 82%

“…It is rather difficult to give a comprehensive list of related works on the subject now. For an overview in the framework of Fock spaces, which we are interested in, one may consult the materials for example in [4,5,9,11,14] and the references therein. On the other hand, over the unit disc of the complex plane or the unit ball in C n , the monographs in [7,10,18] provide a comprehensive expositions specially on the early developments of the area.…”

Section: Introductionmentioning

confidence: 99%

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Topological and dynamical properties of composition operators

Mengestie,

Seyoum

2019

Preprint

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We study various properties of composition operators acting between generalized Fock spaces F p ϕ and F q ϕ with weight functions ϕ grow faster than the classical Gaussian weight function 1 2 |z| 2 and satisfy some mild smoothness conditions. We have shown that if p = q, then the composition operator C ψ : F p ϕ → F q ϕ is bounded if and only if it is compact. This result shows a significance difference with the analogous result for the case when C ψ acts between the classical Fock spaces or generalized Fock spaces where the weight functions grow slower than the Gaussian weight function. We further described the Schatten S p (F 2 ϕ ) class, normal, unitary, cyclic and supercyclic composition operators. As an application, we characterized the compact differences, the isolated and essentially isolated points, and connected components of the space of the operators under the operator norm topology.

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“…On the classical Fock space, these results were proved recently in [11]. Our result now shows that these properties are independent of the fast growth of the inducing weight function ϕ.…”

Section: Essential Norms and Schatten Class Membershipsupporting

confidence: 69%

Section: Essential Norms and Schatten Class Membershipmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

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Topological and dynamical properties of composition operators

Mengestie,

Seyoum

2019

Preprint

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“…Recently, much progress was made in the study of composition operators on Fock spaces (see, for instance, [5,6,11]). One of the main differences between operators C ϕ on Fock spaces and those on the above-mentioned spaces of holomorphic functions on the unit disc or the unit ball is the lack of bounded holomorphic functions in the Fock space setting.…”

Section: Introductionmentioning

confidence: 99%

Topological Structure of the Space of Composition Operators Between Different Fock Spaces

Khoi

Thom

Tien

2021

Complex Anal. Oper. Theory

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“…The study of the boundedness and compactness of the composition operator C ϕ in various function spaces over the unit disc and more general domains is a classical problem studied by many researchers. Without claiming for completeness, we mention the following spaces and references: the Besov space, 1‐4 Bloch space

scriptB

, 5‐8 Dirichlet space

scriptD

, 9‐15 BMOA, 7,8,16‐18 Hardy space H p , 19‐24 Bergman space

{scriptA}^{p}

and the weighted Bergman space

{scriptA}_{α}^{p}

, 19,20,25 Fock space, 26‐29 among others.…”

Section: Introductionmentioning

confidence: 99%

Holomorphic Hölder‐type spaces and composition operators

Karapetyants

Restrepo

2020

Math Methods in App Sciences

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We study boundedness and compactness of composition operators in the generalized Hölder-type space of holomorphic functions in the unit disc with prescribed modulus of continuity. We also devote a significant part of the article to outline some embeddings between such Hölder-type spaces, to discuss properties of modulus of continuity and to construct some useful examples. KEYWORDS composition operators, Hölder spaces, holomorphic functions, modulus of continuity MSC CLASSIFICATION 47B33; 46E15; 30H99 1 INTRODUCTION Let D stand for the unit disc in complex plane C. Given a holomorphic function ∶ D → D by C , we denote the linear composition operator C f(z) ∶= f• (z) = f((z)). The study of the boundedness and compactness of the composition operator C in various function spaces over the unit disc and more general domains is a classical problem studied by many researchers. Without claiming for completeness, we mention the following spaces and references: the Besov space, 1-4

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Some characterizations for composition operators on the Fock spaces

Cited by 14 publications

References 19 publications

Topological and dynamical properties of composition operators

Topological and dynamical properties of composition operators

Topological Structure of the Space of Composition Operators Between Different Fock Spaces

Holomorphic Hölder‐type spaces and composition operators

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