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<p>We characterize the topologizability and power boundedness of convolution and dual convolution operators on power series spaces. We determine necessary conditions for a Toeplitz operator to be m-topologizable, and power bounded on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Lambda _{1}(n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Λ</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Lambda _{\infty }(n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Λ</mi> <mi>∞</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, and consequently on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(H(\mathbb {C})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H(\mathbb {D})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">D</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Topologizability and Power Boundedness of Convolutions and Toeplitz Operators on Power Series Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月18日

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  • Nazlı Doğan

摘要

We characterize the topologizability and power boundedness of convolution and dual convolution operators on power series spaces. We determine necessary conditions for a Toeplitz operator to be m-topologizable, and power bounded on \(\Lambda _{1}(n)\) Λ 1 ( n ) and \(\Lambda _{\infty }(n)\) Λ ∞ ( n ) , and consequently on \(H(\mathbb {C})\) H ( C ) and \(H(\mathbb {D})\) H ( D ) .