Essential Norm of Products of Volterra-Type Operators and Composition Operators on Iterated Banach-Type Spaces

Essential Norm of Products of Volterra-Type Operators and Composition Operators on Iterated Banach-Type Spaces

Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></semantics...

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Bibliographic Details
Main Authors:	Rabab Alyusof, Shams Alyusof, Nacir Hmidouch
Format:	Article
Language:	English
Published:	MDPI AG 2025-05-01
Series:	Axioms
Subjects:	?<sub><i>μ</i>,<i>n</i></sub> ?<sub><i>n</i></sub> products of volterra-type operators and composition operators essential norm
Online Access:	https://www.mdpi.com/2075-1680/14/5/352
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Summary:	Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow></semantics></math></inline-formula> be the set of analytic functions on the open unit disk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">D</mi></semantics></math></inline-formula>. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>∈</mo><msub><mi mathvariant="double-struck">N</mi><mn>0</mn></msub><mo>:</mo><mo>=</mo><mi mathvariant="double-struck">N</mi><mo>∪</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow></mrow></semantics></math></inline-formula>, define the iterated weighted-type Banach space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">V</mi><mi>n</mi></msub><mo>:</mo><mo>=</mo><mfenced separators="" open="{" close="}"><mi>f</mi><mo>∈</mo><mi>H</mi><mrow><mo>(</mo><mi mathvariant="double-struck">D</mi><mo>)</mo></mrow><mo>:</mo><msub><mo movablelimits="true" form="prefix">sup</mo><mrow><mi>z</mi><mo>∈</mo><mi mathvariant="double-struck">D</mi></mrow></msub><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mo>\|</mo><mi>z</mi><mo>\|</mo></mrow><mn>2</mn></msup><mrow><mo>)</mo><mo>\|</mo></mrow><msup><mi>f</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup><mrow><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>\|</mo><mo><</mo><mo>∞</mo></mrow></mfenced><mo>.</mo></mrow></semantics></math></inline-formula> In this work, we study the boundedness and the essential norm of products of Volterra-type operators and composition operators on iterated weighted-type Banach spaces.
ISSN:	2075-1680