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<p>For a continuous endomorphism <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ \omega $</EquationSource> </InlineEquation> on a&#xa0;Banach algebra,we define <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$ \omega_{\mathcal{L}} $</EquationSource> </InlineEquation>-Helemskii biflatness and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$ \omega_{\mathcal{L}} $</EquationSource> </InlineEquation>-amenability for Banach algebrasand then consider the relations between these notions.Moreover, we show that <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$ l^{1}(𝕅_{\vee}) $</EquationSource> </InlineEquation> enjoys <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$ \omega_{\mathcal{L}} $</EquationSource> </InlineEquation>-Helemskii biflatness.</p>

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\( \omega_{\mathcal{L}} \)-Helemskii Biflat Banach Algebras and \( \omega_{\mathcal{L}} \)-Amenable Banach Algebras

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Z. Ghorbani

摘要

For a continuous endomorphism $ \omega $ on a Banach algebra,we define $ \omega_{\mathcal{L}} $ -Helemskii biflatness and $ \omega_{\mathcal{L}} $ -amenability for Banach algebrasand then consider the relations between these notions.Moreover, we show that $ l^{1}(𝕅_{\vee}) $ enjoys $ \omega_{\mathcal{L}} $ -Helemskii biflatness.