Composition Operators on Spaces of Analytic Functions

Cowen, Carl C.; MacCluer, Barbara D.

doi:10.1201/9781315139920

Cited by 564 publications

(407 citation statements)

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“…The proof of the lemma below can be shown by a similar argument as [, Proposition 3.11], consequently we omit the details. Lemma Let

0 < α, β < \infty

and let

φ : [0, \infty) \to [0, \infty)

be an

scriptN

‐function.…”

Section: The Essential Norm Of Bold-italicpϕboldg−boldpψboldh:boldhα∞mentioning

confidence: 98%

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New characterizations for differences of Volterra‐type operators from α‐weighted‐type space to β‐Bloch–Orlicz space

Liang

Cui

2018

Mathematische Nachrichten

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Firstly, we presented three equivalent characterizations for the boundedness of the difference of general Volterra‐type operators from α‐weighted‐type space to β‐Bloch–Orlicz space. Especially, the descriptions in terms of the n‐th power of the induced analytic self‐maps were described. And then we estimated their essential norms, which can provide new compactness criteria and be seen as generalizations of classical results. Finally, we completed this paper with similar results on the differences of other three integral‐type operators, which extend and strengthen several existing results in the literature.

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“…The proof of the lemma below can be shown by a similar argument as [, Proposition 3.11], consequently we omit the details. Lemma Let

0 < α, β < \infty

and let

φ : [0, \infty) \to [0, \infty)

be an

scriptN

‐function.…”

Section: The Essential Norm Of Bold-italicpϕboldg−boldpψboldh:boldhα∞mentioning

confidence: 98%

“…For an analytic self‐map

ϕ : D \to D

, the composition operator

C_{ϕ} : H false(boldD false) \to H false(boldD false)

is defined by

C_{ϕ} f = f \circ ϕ, f \in H false(boldD false) .

The study of composition operators is a fairly active field. For general references on the theory of composition operators, see the famous books by Cowen and MacCluer and by Shapiro.…”

Section: Introductionmentioning

confidence: 99%

New characterizations for differences of Volterra‐type operators from α‐weighted‐type space to β‐Bloch–Orlicz space

Liang

Cui

2018

Mathematische Nachrichten

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“…If the weighted composition operator is bounded on (), then the adjoint of satisfies For , by the Schwarz-Pick theorem in [26], for any .…”

Section: Compact Differencementioning

confidence: 99%

Compact differences of weighted composition operators on the weighted Bergman spaces

2017

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“…Every analytic selfmap ϕ: D → D of the unit disc induces a composition operator C ϕ : H(D) → H(D), given by C ϕ f = f • ϕ. For general information of composition operators on classical spaces of analytic functions the reader is referred to the excellent monographs by Cowen and MacCluer [7] and Shapiro [19]. Throughout this paper we assume that ϕ(0) = 0 and 0 < |ϕ (0)| < 1, and study the Königs eigenfunction σ ∈ H(D) for the operator C ϕ : H(D) → H (D).…”

Section: Introductionmentioning

confidence: 99%

Königs eigenfunction for composition operators on Bloch and H∞ type spaces

Eklund

Galindo

Lindström

2017

Journal of Mathematical Analysis and Applications

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To Richard Aron on the occasion of his retirement, with very much appreciation Keywords: Composition operator Königs eigenfunctionWe discuss when the Königs eigenfunction associated with a non-automorphic selfmap of the complex unit disc that fixes the origin belongs to Banach spaces of holomorphic functions of Bloch and H ∞ type. In the latter case, our characterization answers a question of P. Bourdon. Some spectral properties of composition operators on H ∞ for unbounded Königs eigenfunction are obtained.

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Composition Operators on Spaces of Analytic Functions

Cited by 564 publications

References 0 publications

New characterizations for differences of Volterra‐type operators from α‐weighted‐type space to β‐Bloch–Orlicz space

New characterizations for differences of Volterra‐type operators from α‐weighted‐type space to β‐Bloch–Orlicz space

Compact differences of weighted composition operators on the weighted Bergman spaces

Königs eigenfunction for composition operators on Bloch and H∞ type spaces

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