Invariant Subspaces of the Integration Operators on Hörmander Algebras and Korenblum Type Spaces

Bonet, José; Galbis, Antonio

doi:10.1007/s00020-020-02593-6

Cited by 2 publications

(2 citation statements)

References 33 publications

(38 reference statements)

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“…The weight v(z) := exp(−|z| α ), α > 1, on the complex plane satisfies the assumption of Theorem 39. Galbis and the author utilized the results of Abanin and Tien to describe in [53] the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of analytic functions on the unit disc or the complex plane, in particular for Korenblum type spaces and for Hörmander algebras of entire functions.…”

Section: Lemma 38 Let E Be a Banach Space Of Analytic Functions On Th...mentioning

confidence: 99%

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

Bonet

2022

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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In this survey we report about recent work on weighted Banach spaces of analytic functions on the unit disc and on the whole complex plane defined with sup-norms and operators between them. Results about the solid hull and core of these spaces and distance formulas are reviewed. Differentiation and integration operators, Cesàro and Volterra operators, weighted composition and superposition operators and Toeplitz operators on these spaces are analyzed. Boundedness, compactness, the spectrum, hypercyclicity and (uniform) mean ergodicity of these operators are considered.

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Section: Lemma 38 Let E Be a Banach Space Of Analytic Functions On Th...mentioning

confidence: 99%

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

Bonet

2022

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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“…For any pair 0 < µ < α < ∞ , the canonical inclusion map ι µ,α : [2,11,12]. The Volterra integral operator acting on a growth Fréchet or (LB)-space has been investigated by Bonet [9] in terms of continuity, compactness, and spectrum.…”

Section: Introductionmentioning

confidence: 99%

Operators between different weighted Fréchet and (LB)-spaces of analytic functions

Kızgut¹

2021

Turk J Math

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We study some classical operators defined on the weighted Bergman Fréchet space A p α+ (resp. weighted Bergman (LB)-space A p α− ) arising as the projective limit (resp. inductive limit) of the standard weighted Bergman spaces into the growth Fréchet space H ∞ α+ (resp. growth (LB)-space H ∞ α− ), which is the projective limit (resp. inductive limit) of the growth Banach spaces. We show that, for an analytic self map φ of the unit disc D , the continuities of the weighted composition operator Wg,φ , the Volterra integral operator Tg , and the pointwise multiplication operator Mg defined via the identical symbol function are characterized by the same condition determined by the symbol's state of belonging to a Bloch-type space. These results have consequences related to the invertibility of Wg,φ acting on a weighted Bergman Fréchet or (LB)-space. Some results concerning eigenvalues of such composition operators Cφ are presented.

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Invariant Subspaces of the Integration Operators on Hörmander Algebras and Korenblum Type Spaces

Cited by 2 publications

References 33 publications

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

Operators between different weighted Fréchet and (LB)-spaces of analytic functions

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